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SUMMARY:Journée “Jeunes analystes et modélisateurs lyonnais”.
DTSTART;VALUE=DATE-TIME:20221129T130000Z
DTEND;VALUE=DATE-TIME:20221129T161500Z
DTSTAMP;VALUE=DATE-TIME:20230129T093500Z
UID:indico-event-8031@indico.math.cnrs.fr
DESCRIPTION:Speakers: Maria Eugenia Martinez (CMM)\, Billel Guelmame (UMPA
\, ENS Lyon.)\, Laurent Lafleche (ICJ - Université Claude Bernard Lyon 1)
\, Michèle Romanos (Institut de Mathématiques de Toulouse (UT3))\n\n14h0
0. Michèle Romanos : "Multi-tissue viscous models for tissue growth: inco
mpressible limit\, qualitative behaviour at the limit\, and applications t
o the elongation of the vertebrate embryo."14h45. Maria Eugenia Martinez :
" The soliton problem for the Zakharov water waves system with a slowly v
arying bottom."15h30. Pause.15h45. Laurent Laflèche : "On Semiclassical S
obolev inequalities."16h30. Billel Guelmame : "On some regularized nonline
ar hyperbolic equations." Title: Multi-tissue viscous models for tissue
growth: incompressible limit\, qualitative behaviour at the limit\, and a
pplications to the elongation of the vertebrate embryo.Abstract: during ve
rtebrate embryo elongation\, neural and muscular tissues grow in contact w
hile remaining segregated\, and the live imaging of these tissues reveals
cellular turbulent behavior. To understand such behaviors\, we introduce t
wo 2D mechanical models modeling the evolution of two viscous tissues in c
ontact. Their main property is to model the swirling cell motions while ke
eping the tissues segregated\, as observed during embryonic development. S
egregation is encoded differently in the two models: by passive or active
segregation (based on a mechanical repulsion pressure). We formally comput
e the incompressible limits of the two models\, and obtain strictly segreg
ated solutions. The two models thus obtained are compared and a well-posed
ness and regularity analysis is conducted. Two striking features in the ac
tive segregation model are revealed: the persistence of the repulsion pres
sure at the limit (ghost effect) and a pressure jump at the tissues' bound
aries. The results are supported by numerical simulations in 2D and confro
nted to the biological data. Inspired by these models\, we exhibit a final
model which incorporates additional biological terms such as the addition
of new cells into the tissues. We calibrate this model using the biologic
al data at hand\, and simulate the elongation of the vertebrate embryo. In
teresting biological hypotheses arise from the numerical exploration of th
e model parameters\, which we then confirm experimentally on quail embryos
. Title: The soliton problem for the Zakharov water waves system with a s
lowly varying bottom. Abtract: Zakharov water waves arises as a free surf
ace model for an irrotational and incompressible fluid under the influence
of gravity. Such fluid is considered in a domain with rigid bottom (descr
ibed as ha(x)) and a free surface. When considering the pressure over the
surface\, Amick-Kirchgässner proved the existence of solitary waves Qc (s
olutions that maintain its shape as they travel in time) of speed c for th
e flat-bottom case (a=1). In this talk\, we are interested in the analysi
s of the behavior of the solitary wave solution of the flat-bottom problem
when the bottom actually presents a (slight) change at some point. We con
struct a solution to the Zakharov water waves system with non-flat bottom
that is time assympotic (as time t tends to - infinity) to the Amick-Kirch
gässner soliton Q_c. Title: On Semiclassical Sobolev inequalities.Abst
ract: in the context of combined mean-field and semiclassical limits\, suc
h as the limit from the N-body Schrödinger equation to the Hartree--Fock
and Vlasov equations\, it is useful to obtain inequalities uniform in the
Planck constant and the number of particles. It is therefore important to
obtain analogous tool and inequalities in the context of quantum mechanics
\, such as operator versions of Wasserstein\, Lebesgue and Sobolev distanc
es\, and the corresponding classical inequalities.In this talk\, I will pr
esent the quantum version of the phase space Sobolev spaces\, as well as t
he corresponding Sobolev inequalities\, other related inequalities and som
e applications to quantum optimal transport\, and mean-field and semiclass
ical limits. Title: On some regularized nonlinear hyperbolic equations.A
bstract: it is known that the solutions of nonlinear hyperbolic partial di
fferential equations develop discontinuous shocks in finite time even with
smooth initial data. Those shock are problematic in the theoretical study
and in the numerical computations. To avoid these shocks\, many regulariz
ations have been studied in the literature. For example\, adding diffusion
and/or dispersion to the equation. In this talk\, we present and study so
me non-diffusive and non-dispersive regularizations of the Burgers equatio
n and the barotropic Euler equations that have similar properties as the
classical equations.\n\nhttps://indico.math.cnrs.fr/event/8031/
LOCATION:Fokko (ICJ)
URL:https://indico.math.cnrs.fr/event/8031/
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