Cahiers du CEREMADE

Unité Mixte de Recherche du C.N.R.S. N°7534
 
Abstract : We study the limit as $e o 0$ of the entropy solutions of the equation $p_t ue + dv_xleft[Aleft(frac{x}{e},ue ight) ight] =0$. We prove that the sequence $ue$ two-scale converges towards a function $u(t,x,y)$, and $u$ is the unique solution of a limit evolution problem. The remarkable point is that the limit problem is not a scalar conservation law, but rather a kinetic equation in which the macroscopic and microscopic variables are mixed. We also prove a strong convergence result in $L^1_{ ext{loc}}$.
 
 
Homogenization of nonlinear scalar conservation laws
DALIBARD Anne-Laure
2007-26
14-06-2007
 
Université de PARIS - DAUPHINE
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