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BEGIN:VEVENT
SUMMARY:Convergence to equilibrium for gradient-like systems with analytic
features
DTSTART;VALUE=DATE-TIME:20160615T143000Z
DTEND;VALUE=DATE-TIME:20160615T150500Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2982@indico.math.cnrs.fr
DESCRIPTION:Speakers: Morgan Pierre (Laboratoire de Mathématiques et Appl
ications)\nA celebrated result of S. Lojasiewicz states that every bounded
solution of a gradient flow associated to an analytic function converges
to a steady state as time goes to infinity. Convergence rates can also be
obtained. These convergence results have been generalized to a large varie
ty of finite or infinite dimensional gradient-like flows. The fundamental
example in infinite dimension is the semilinear heat equation with an anal
ytic nonlinearity. In this talk\, we show how some of these results can be
adapted to time discretizations of gradient-like flows\, in view of appli
cations to PDEs such as the Allen-Cahn equation\, the sine-Gordon equation
\, the Cahn-Hilliard equation\, the Swift-Hohenberg equation\, or the phas
e-field crystal equation.\n\nhttps://indico.math.cnrs.fr/event/939/contrib
utions/2982/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2982/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Entropy methods for degenerate diffusions and weighted functional
inequalities
DTSTART;VALUE=DATE-TIME:20160617T132500Z
DTEND;VALUE=DATE-TIME:20160617T140000Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2981@indico.math.cnrs.fr
DESCRIPTION:Speakers: Bruno Nazaret (SAMM - Statistique\, Analyse\, Modél
isation multidisciplinaire)\nWe will present results on large time asympto
tics for some fast diffusion equations with power law weights. We will sho
w that\, for such diffusions\, new phenomena appear : the asymptotic rates
of convergence\, obtained by linearization\, are not global\, the underly
ing functional inequalities may experience symmetry breaking and the Baren
blatt self-similar profiles is not optimal.\n\nhttps://indico.math.cnrs.fr
/event/939/contributions/2981/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2981/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Asymptotic analysis for a simplified model of model of dynamical p
erfect plasticity
DTSTART;VALUE=DATE-TIME:20160616T132500Z
DTEND;VALUE=DATE-TIME:20160616T140000Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2980@indico.math.cnrs.fr
DESCRIPTION:Speakers: Clément Mifsud (Laboratoire Jacques Louis Lions)\nI
n this talk\, we will present an initial boundary value problem for a hype
rbolic system under constraints\, coming from mechanics. To study the solu
tions of such a system\, we will use a viscous approach that relaxes the c
onstraints. We will explain the asymptotic analysis\, when the viscous par
ameter tends to zero\, which leads to an interaction between the boundary
condition and the constraints for the constrained system. If time permits\
, we will show some numerical results.\n\nhttps://indico.math.cnrs.fr/even
t/939/contributions/2980/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2980/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Global existence for small data of the viscous Green-Naghdi equati
ons
DTSTART;VALUE=DATE-TIME:20160615T132000Z
DTEND;VALUE=DATE-TIME:20160615T135500Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2979@indico.math.cnrs.fr
DESCRIPTION:Speakers: Dena Kazerani (Laboratoire Jacques-Louis Lions)\nWe
consider the Cauchy problem for the Green-Naghdi equations with viscosity\
, for small initial data. It is well-known that adding a second order diss
ipative term to a hyperbolic system leads to the existence of global smoot
h solutions\, once the hyperbolic system is symmetrizable and the so-calle
d Kawashima-Shizuta condition is satisfied. We first show that the Green-N
aghdi equations can be written in a symmetric form\, using the associated
Hamiltonian. This system being dispersive\, in the sense that it involves
third order derivatives\, the symmetric form is based on symmetric differe
ntial operators. Then\, we use this structure for an appropriate change of
variable to prove that adding viscosity effects through a second order te
rm leads to global existence of smooth solutions\, for small data. We also
deduce that constant solutions are asymptotically stable.\n\nhttps://indi
co.math.cnrs.fr/event/939/contributions/2979/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2979/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Global Existence of Solutions to the 3D Navier-Stokes Equations wi
th Degenerate Viscosities
DTSTART;VALUE=DATE-TIME:20160615T081000Z
DTEND;VALUE=DATE-TIME:20160615T085500Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2978@indico.math.cnrs.fr
DESCRIPTION:Speakers: Alexis Vasseur (Department of Mathematics)\nWe prove
the existence of global weak solutions for 3D compressible Navier-Stokes
equations with degenerate viscosities. The method is based on the Bresch
and Desjardins entropy. The solutions are obtained as limits of the quanti
c Navier-Stokes system. The main contribution is to derive the Mellet-Vass
eur type inequality for the weak\nsolutions\, even if it is not verified b
y the first level of approximation. This provides existence of global solu
tions in time\, for the compressible Navier-Stokes equations\, for any gam
ma bigger than one\, in three dimensional space\, with large initial data\
, possibly vanishing on the vacuum. This is a joint work with Cheng Yu. Th
e paper will appear in Inventiones.\n\nhttps://indico.math.cnrs.fr/event/9
39/contributions/2978/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2978/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Implicit-explicit linear multistep methods for stiff kinetic equat
ions
DTSTART;VALUE=DATE-TIME:20160616T073000Z
DTEND;VALUE=DATE-TIME:20160616T081500Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2976@indico.math.cnrs.fr
DESCRIPTION:Speakers: Giacomo Dimarco (Department of Mathematics and Compu
ter Science)\nWe consider the development of high order asymptotic-preserv
ing linear multistep methods for kinetic equations and related problems. T
he methods are first developed for BGK-like kinetic models and then extend
ed to the case of the full Boltzmann equation. The behavior of the schemes
in the Navier-Stokes regime is also studied and compatibility conditions
derived. We show that\, compared to IMEX Runge-Kutta methods\, the IMEX mu
ltistep schemes have several advantages due to the absence of coupling con
ditions and to the greater computational efficiency. The latter is of para
mount importance when dealing with the time discretization of multidimensi
onal kinetic equations.\n\nhttps://indico.math.cnrs.fr/event/939/contribut
ions/2976/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2976/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A multiscale numerical approach for a class of time-space oscillat
ory problems
DTSTART;VALUE=DATE-TIME:20160615T123500Z
DTEND;VALUE=DATE-TIME:20160615T132000Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2975@indico.math.cnrs.fr
DESCRIPTION:Speakers: Mohammed Lemou (Institut de Recherche Mathématiques
de Rennes)\nHigh oscillations may arise in many physical problems: Schrö
dinger equations\, kinetic equations\, or more generally high frequency wa
ves. In this talk\, we will present a general strategy that allows the con
struction of uniformly (with respect to the oscillation frequency) accurat
e numerical schemes in the following situations:\ni) time oscillations wit
h applications to kinetic and Schrödinger equations.\nii) time-space os
cillations with applications to some high frequency waves and semi-classic
al quantum models.\nSome numerical tests will be presented to illustrate t
he efficiency of the strategy.\n\nhttps://indico.math.cnrs.fr/event/939/co
ntributions/2975/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2975/
END:VEVENT
BEGIN:VEVENT
SUMMARY:A (mainly numerical) study of a hyperbolic model for chemotaxis
DTSTART;VALUE=DATE-TIME:20160615T093000Z
DTEND;VALUE=DATE-TIME:20160615T101500Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2974@indico.math.cnrs.fr
DESCRIPTION:Speakers: Magali Ribot (Laboratoire de Mathématiques - Analys
e\, Probabilités\, Modélisation - Orléans)\nThe aim of this talk is to
give some first results on the behaviour of the solutions of a 1D hyperbol
ic type chemotaxis system\, based on incompressible Euler equation. More p
recisely\, I will completely describe the stationary solutions with vacuum
for this system and I will study numerically the stability of these stead
y states after the presentation of an adapted numerical scheme. A comparis
on with a limit parabolic system will also be performed.\n\nhttps://indico
.math.cnrs.fr/event/939/contributions/2974/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2974/
END:VEVENT
BEGIN:VEVENT
SUMMARY:From particle methods to hybrid semi-Lagrangian schemes
DTSTART;VALUE=DATE-TIME:20160616T081500Z
DTEND;VALUE=DATE-TIME:20160616T090000Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2973@indico.math.cnrs.fr
DESCRIPTION:Speakers: Frédérique Charles (Laboratoire Jacques-Louis Lion
s)\nParticle methods for transport equations consist in pushing forward pa
rticles along the characteristic lines of the flow\, and to describe then
the transported density as a sum of weighted and smoothed particles. Conce
ptually simple\, standard particle methods have the main drawback to produ
ce noisy solutions or to require frequent remapping.\n\nIn this talk we pr
esent two classes of particle methods which aim at improving the accuracy
of the numerical approximations with a minimal amount of smoothing.\n\nThe
idea of the Linearly Transformed Particle method is to transform the shap
e functions of particles in order to follow the local variation of the flo
w. This method has been adapted and analyzed for the Vlasov- Poisson syste
m and for a compressible aggregation equation. In both cases the error est
imate is improved compared to classical particle methods\, with the gain o
f a strong convergence of the numerical solution.\n\nHowever\, for long re
mapping periods\, shapes of particles could become to much stretched out.
The second method solve this problem of locality by combining a backward s
emi-Lagrangian approach and local linearizations of the flow. The converge
nce properties are improved and validated by numerical experiments.\nThis
is a joint work with Martin Campos-Pinto (LJLL\, UPMC).\n\nhttps://indico.
math.cnrs.fr/event/939/contributions/2973/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2973/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Modelling and numerical approximation for the nonconservative bi-t
emperature MHD model
DTSTART;VALUE=DATE-TIME:20160615T101500Z
DTEND;VALUE=DATE-TIME:20160615T105000Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2972@indico.math.cnrs.fr
DESCRIPTION:Speakers: Xavier Lhebrard (Centre Lasers Intenses et Applicati
ons)\nIn order to achieve inertial confinement fusion\, one has to improve
the knowledge of the laser-plasma interaction. There exists two main ways
of describing this phenomenon\, the microscopic (kinetic) approach and th
e macroscopic (hydrodynamic) approach. The kinetic approach is not competi
tive since it is too expensive in computational time. This is why we inves
tigate an intermediate model in thermal nonequilibrium\, which is between
the kinetic model and the hydrodynamic model.\n\nIn the first stage of the
confinement the magnetic field is negligible\, the relevant intermediate
model is than the nonconservative bitemperature Euler model. Recently in [
1]\, an entropic approximation of this system has been derived thanks to n
umerical schemes based on an underlying conservative kinetic model.\n\nHow
ever in the last stage of the confinement the target is penetrated by rela
tivistic electrons\, which induces a strongly variable magnetic field. Thi
s is why we want to deal with an intermediate model which takes into accou
nt the magnetic field.\n\nIn this work we propose to study a bitemperature
MHD model. This system consists in four conservation equations for mass\,
impulsion and magnetic field and two nonconservation equations\, that is
to say\, one for each energy. Physically\, the model describes the interac
tion of a mixture of one species of ions and one species of electrons in t
hermal nonequilibrium subjected to a transverse variable magnetic field.\n
\nA first result is to have been able to established the hydrodynamic mode
l from an underlying kinetic model. More precisely\, using an out of equil
ibrium Chapman-Enskop procedure\, the bitemperature MHD model is construct
ed from a BGK model coupled with Maxwell equations with full Lorentz force
\, which includes the magnetic field.\n\nFinally\, we approximate the weak
solutions of the bitemperature MHD model using a kinetic scheme\, based o
n the underlying kinetic model.\n\n\n\nReferences\n\n[1] D. Aregba-Driolle
t\, S. Brull\, J.Breil\, B. Dubroca and E. Estibal\, Modelling and numeric
al ap-\nproximation for the nonconservative bitemperature Euler model\, pr
eprint\, 2015.\n\nhttps://indico.math.cnrs.fr/event/939/contributions/2972
/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2972/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Time splitting methods and the semi-classical limit for nonlinear
Schrödinger equations
DTSTART;VALUE=DATE-TIME:20160616T093000Z
DTEND;VALUE=DATE-TIME:20160616T101500Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2971@indico.math.cnrs.fr
DESCRIPTION:Speakers: Rémi Carles (Institut Montpelliérain Alexander Gro
thendieck)\nWe consider the time discretization based on Lie-Trotter split
ting\, for the nonlinear Schrödinger equation\, in the semi-classical lim
it\, with initial data under the form of WKB states. Both the exact and th
e numerical solutions keep a WKB structure\, on a time interval independen
t of the Planck constant. We prove error estimates\, which show that the q
uadratic observables can be computed with a time step independent of the P
lanck constant. We give a flavor of the functional framework\, based on t
ime-dependent analytic spaces.\n\nhttps://indico.math.cnrs.fr/event/939/co
ntributions/2971/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2971/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Non linear stability of Minkowski space-time with massive scalar f
ield
DTSTART;VALUE=DATE-TIME:20160617T101000Z
DTEND;VALUE=DATE-TIME:20160617T104500Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2970@indico.math.cnrs.fr
DESCRIPTION:Speakers: Yue Ma (School of Mathematics and Statistics)\nIn th
is talk we will present some recent work about the system of Einstein equa
tion coupled with a massive scalar field and the system of $f(R)$ field eq
uation (partially published in [2]). More precisely\, on the nonlinear glo
bal stability of the Minkowski space-time within these two similar context
s. In a PDE point of view\, they are equivalent to the global existence of
a special class of quasi-linear wave-Klein-Gordon system with small initi
al data.\n\nTo the author’s knowledge there is not so much choice to dea
l with this kind of system (for a detailed explication of the major diffic
ulty\, see for example in [1] page 2)\, and we apply the “hyperboloidal
foliation method” introduced by the author in [1] combined with some new
ly developed tools such as $L^∞$ estimates on Klein-Gordon equations in
curved space-time and $L^∞$ estimates on wave equations based on the exp
ression of spherical means. We also adapt some tools developed in classica
l framework for the analysis of Einstein equation into our hyperboloidal f
oliation framework\, such as the estimates based on wave gauge conditions
and the L$^∞$ estimates on wave equations based on integration along cha
racteristics.\n\n\nReferences\n\n[1] P. LeFloch and Y. Ma\, The hyperboloi
dal foliation method\, World Scientific\, 2015\n\n[2] P. LeFloch and Y. Ma
\, The nonlinear stability of Minkowski space for self-gravitating massive
field. The\nwave-Klein-Gordon model\, Comm. Math. Phys.\, published onlin
e.\n\nhttps://indico.math.cnrs.fr/event/939/contributions/2970/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2970/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Uniform asymptotic preserving scheme for hyperbolic systems in 2D
DTSTART;VALUE=DATE-TIME:20160617T081500Z
DTEND;VALUE=DATE-TIME:20160617T085000Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2969@indico.math.cnrs.fr
DESCRIPTION:Speakers: Emmanuel Franck (Inria Nancy Grand-est)\nIn this wor
k\, we are interested by the discretization of hyperbolic system with stif
f source term. Firstly we consider a simple linear case : the damped wave
equation which can be approximative by a diffusion equation at the limit.
For this equation we propose a asymptotic preserving scheme which converge
uniformly on general and unstructured 2D meshes contrary to the classical
extension of the AP which are not consistent in the limit regime on unstr
uctured meshes. After that we propose to extend this method to a nonlinear
problem: the Euler equations with friction. At the end the link with the
well-balanced scheme (for Euler-Poisson) will be introduced.\n\nhttps://in
dico.math.cnrs.fr/event/939/contributions/2969/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2969/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Complete flux schemes for conservation laws of advection-diffusion
-reaction type
DTSTART;VALUE=DATE-TIME:20160617T092500Z
DTEND;VALUE=DATE-TIME:20160617T101000Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2968@indico.math.cnrs.fr
DESCRIPTION:Speakers: Jan ten Thije Boonkkamp (Department of Mathematics a
nd Computer Science)\nComplete flux schemes are recently developed numeric
al flux approximation schemes for conservation laws of advection-diffusion
-reaction type\; see e.g. [1\, 2]. The basic complete flux scheme is deriv
ed from a local one-dimensional boundary value problem for the entire equa
tion\, including the source term. Consequently\, the integral representati
on of the flux contains a homogeneous and an inhomogeneous part\, correspo
nding to the advection-diffusion operator and the source term\, respective
ly. Suitable quadrature rules give the numerical flux.\n\nFor time-depende
nt problems\, the time derivative is considered a source term and is inclu
ded in the inhomogeneous flux\, resulting in an implicit semi-discretisati
on. The implicit system proves to have much smaller dissipation and disper
sion errors than the standard semidiscrete system\, especially for dominan
t advection.\n\nJust as for scalar equations\, for coupled systems of cons
ervation laws\, the complete flux approximation is derived from a local sy
stem boundary value problem\, this way incorporatin the coupling between t
he constituent equations in the discretization. Also in the system case\,
the numerical flux (vector) is the superpostion of a homogeneous and an in
homogeneous component\, corresponding to the advection-diffusion operator
and the source term vector\, respectively. The scheme is applied to multi-
species diffusion and satisfies the mass constraint exactly.\n\n\n\nRefere
nces\n\n[1] J.H.M. ten Thije Boonkkamp and M.J.H. Anthonissen\, The finite
volume-complete flux scheme for advection-diffusion-reaction equations\,
J. Sci. Comput. 46\, pp. 47-70 (2011).\n\n[2] J.H.M. ten Thije Boonkkamp\,
J. van Dijk\, L. Liu and K.S.C. Peerenboom\, Extension of the complete fl
ux scheme to systems of comservation laws\, J. Sci. Comput. 53\, pp. 552-5
68 (2012).\n\nhttps://indico.math.cnrs.fr/event/939/contributions/2968/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2968/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Numerical convergence rate for the diffusive limit of the p-system
with damping
DTSTART;VALUE=DATE-TIME:20160615T150500Z
DTEND;VALUE=DATE-TIME:20160615T154000Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2967@indico.math.cnrs.fr
DESCRIPTION:Speakers: Hélène Mathis (Laboratoire de Mathématiques Jean
Leray)\nWe are interested in the study of the diffusive limit of the $p$-s
ystem with damping and its approximation by an Asymptotic Preserving (AP)
Finite Volume scheme. Provided the system is endowed with an entropy-entro
py flux pair\, we give the convergence rate of classical solutions of the
p-system with damping towards the smooth solutions of the porous media equ
ation using a relative entropy method. Adopting a semi-discrete scheme\, w
e establish that the convergence rate is preserved by the approximated sol
utions. Several numerical experiments illustrate the relevance of this res
ult.\n\nhttps://indico.math.cnrs.fr/event/939/contributions/2967/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2967/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Stability results of dissipative systems via the frequency domain
approach
DTSTART;VALUE=DATE-TIME:20160617T073000Z
DTEND;VALUE=DATE-TIME:20160617T081500Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2966@indico.math.cnrs.fr
DESCRIPTION:Speakers: Serge Nicaise (Laboratoire de Mathématiques et de l
eurs Applications de Valenciennes)\nThe frequency domain approach goes bac
k to J. Prüss [Trans. Amer. Math. Soc. 284 (1984)\, 847-857] and F. L. Hu
ang [Ann. Differential Equations 1 (1985)\, 43-56] that show that a $C_0$
semigroup $(e^{tA})_{t\\geq 0}$ of contractions in a Hilbert space $H$ is
exponentially stable if and only if the resolvent of $A$ is uniformly boun
ded on the imaginary axis. Afterwards Z. Liu and B. Rao [Z. Angew. Math.
Phys. 56 (2005)\, 630-644]\, C. J. K. Batty and T. Duyckaerts [J. Evol.
Equ. 8 (2008)\, 765-780]\, and\nA. Bátkai\, K.-J. Engel\, J. Prüss and
R. Schnaubelt [Math. Nachr. 279 (2006)\, 1425-1440] have given some suffi
cient conditions on the behavior of the resolvent of $A$ on the imaginary
axis that guarantee an almost polynomial decay of the semigroup. Finally a
n optimal result about the polynomial decay was found by A. A. Borichev an
d Yu. V. Tomilov [Math. Ann. 347 (2010)\, 455-478]. This approach is a pow
erful tool for the study of the decay of the semigroup associated with co
ncrete dissipative systems since it reduces to the study of the resolvent
on the imaginary axis. \n\nIn our talk\, we will first recall these two re
sults and then illustrate them on two particular dissipative systems\, nam
ely a generalized telegraph equation [Z. Angew. Math. Phys. 66 (2015)\, 3
221-3247] and a dispersive medium model (joint work with C. Scheid (Univ.
Nice)).\n\nhttps://indico.math.cnrs.fr/event/939/contributions/2966/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2966/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Dimensional reduction of a multiscale model based on long time asy
mptotics
DTSTART;VALUE=DATE-TIME:20160616T101500Z
DTEND;VALUE=DATE-TIME:20160616T105000Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2965@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marie Postel (Laboratoire Jacques-Louis Lions)\nDepe
nding on their velocity field\, some models lead to moment equations that
enable one to compute monokinetic solutions economically. We detail the ex
ample of a multiscale structured cell population model\, consisting of a s
ystem of 2D transport equations. The reduced model\, a system of 1D transp
ort equations\, is obtained by computing the moments of the 2D model with
respect to one variable. The 1D solution is defined from the solution of t
he 2D model starting from an initial condition that is a Dirac mass in the
direction removed by reduction. Long time properties of the 1D model solu
tion are obtained in connection with properties of the support of the 2D s
olution for general case initial conditions. Finite volume numerical appro
ximations of the 1D reduced model can be used to compute the moments of th
e 2D solution with proper accuracy. The numerical robustness is studied in
the scalar case\, and a full scale vector case is presented.\n\nhttps://i
ndico.math.cnrs.fr/event/939/contributions/2965/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2965/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Global existence and large-time behaviour for reaction-diffusion m
odels
DTSTART;VALUE=DATE-TIME:20160616T124000Z
DTEND;VALUE=DATE-TIME:20160616T132500Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2964@indico.math.cnrs.fr
DESCRIPTION:Speakers: Klemens Fellner (Institut für Mathematik und Wissen
schaftliches Rechnen)\nSystems of nonlinear reaction-diffusion equations a
re encountered frequently as models in chemistry\, physics\, populations d
ynamics and biology. However\, due to the lack of comparison principles fo
r general reaction-diffusion systems\, already the existence of global wea
k/classical solutions poses many open problems\, in particular in 3D.\nIn
the absence of comparison principles\, so called duality methods have rece
ntly proven to be one of the most powerful tools in obtaining global solut
ions for nonlinear reaction-diffusion systems.\nThe first part of this tal
k will present recent advances and results concerning the existence of glo
bal solutions via duality methods. The second part of the talk will then c
onsider reaction-diffusion systems\, which feature an entropy functional a
nd discuss the convergence to equilibrium states with computable rates for
large classes of such reaction-diffusion models.\n\nhttps://indico.math.c
nrs.fr/event/939/contributions/2964/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2964/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Poster session
DTSTART;VALUE=DATE-TIME:20160616T140000Z
DTEND;VALUE=DATE-TIME:20160616T160000Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2963@indico.math.cnrs.fr
DESCRIPTION:Speakers: Ahmed Ait Hammou Oulhaj (Laboratoire Paul Painlevé)
\, An Zhang (CEREMADE)\, Andrea Bondesan (Laboratoire MAP5)\, Judith Beren
dsen (Institute for Computational and Applied Mathematics)\, Maxime Herda
(Institut Camille Jordan)\, Samia Zermani (Institut aux Etudes d'Ingénieu
rs el Manar)\nhttps://indico.math.cnrs.fr/event/939/contributions/2963/
LOCATION: Salle Kampé de Fériet - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2963/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Exponential decay of a finite volume scheme to the thermal equilib
rium for drift-diffusion systems
DTSTART;VALUE=DATE-TIME:20160617T124000Z
DTEND;VALUE=DATE-TIME:20160617T132500Z
DTSTAMP;VALUE=DATE-TIME:20201001T035508Z
UID:indico-contribution-939-2962@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marianne Bessemoulin (Laboratoire de Mathématiques
Jean Leray)\nWe are interested in the large-time behavior of a numerical s
cheme discretizing drift-diffusion systems for semiconductors. The conside
red scheme is finite volume in space\, and the numerical fluxes are a gene
ralization of the classical Scharfetter-Gummel scheme\, which allows to co
nsider both linear or nonlinear pressure laws.\nWe study the convergence o
f approximate solutions towards an approximation of the thermal equilibriu
m state as time tends to infinity\, and obtain a decay rate by controlling
the discrete relative entropy with the entropy production. This result is
proved under assumptions of existence and uniform-in-time $L^\\infty$ est
imates for numerical solutions\, which will be discussed.\nThis is a joine
d work with Claire Chainais-Hillairet.\n\nhttps://indico.math.cnrs.fr/even
t/939/contributions/2962/
LOCATION: Salle de Réunion - Bâtiment M2
URL:https://indico.math.cnrs.fr/event/939/contributions/2962/
END:VEVENT
END:VCALENDAR