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SUMMARY:Dissipative hyperbolic systems and their diffusion large-time beha
viors: Linear cases
DTSTART;VALUE=DATE-TIME:20180711T041500Z
DTEND;VALUE=DATE-TIME:20180711T044500Z
DTSTAMP;VALUE=DATE-TIME:20200403T053914Z
UID:indico-contribution-1763@indico.math.cnrs.fr
DESCRIPTION:Speakers: Tien Thinh NGUYEN (Gran Sasso Science Institute\, It
aly)\nDissipative hyperbolic systems play a central role in many applicati
ons including the kinetic models for gas dynamics and the relaxation numer
ical schemes approximating conservation laws. One important feature of thi
s kind of systems is the diffusion limit of solution as time tends to infi
nity. In this talk\, we will discuss some reasonable dissipative structure
s such that for large time\, the unique solution to the initial value prob
lem for\n\n$$\\partial_tu+\\sum_{j=1}^dA_j\\partial_{x_j}u+Bu=0$$\n\nis ap
proximated by a solution to the initial value problem for a parabolic syst
em\, where $A_j$ and $B$ are $n\\times n$ matrices with real constant entr
ies\, and $u=u(x\,t)$ is an $n$-dimensional real vector. The approximation
is of order $\\mathcal O\\bigl(t^{-\\frac d2(\\frac 1q-\\frac 1p)-\\alpha
}\\bigr)$ for $\\alpha\\in\\{1/2\,1\\}$ and $1\\le q\\le p\\le \\infty$\,
up to an exponentially decaying error. This optimal result in [mascianguye
n17\,nguyen18] is a generalization of [bianchini07] at the linear level. T
he main idea is based on the perturbation theory for linear operators and
the Fourier analysis.\n\nIn collaboration with Corrado Mascia (Università
di Roma 1 - Italy).\n\n[bianchini07] S. Bianchini\, B. Hanouzet and R. Na
talini\, Asymptotic behavior of smooth solutions for partially dissipative
hyperbolic systems with a convex entropy\, Comm. Pure Appl. Math.\, 60 (2
007)\, 1559 -- 1622.\n\n[mascianguyen17] C. Mascia and T. T. Nguyen\, $L^p
$-$L^q$ decay estimates for dissipative linear hyperbolic systems in 1D\,
J. Differential Equations\, 263 (2017)\, 6189 -- 6230.\n\n[nguyen18] T. T.
Nguyen\, Asymptotic limit and decay estimates for a class of dissipative
linear hyperbolic systems in several dimensions\, Discrete Contin. Dyn. Sy
st.\, (to appear).\n\nhttps://indico.math.cnrs.fr/event/3023/contributions
/1763/
LOCATION:Ho Chi Minh City University of Science
URL:https://indico.math.cnrs.fr/event/3023/contributions/1763/
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