First Order Singular Perturbations of Quasilinear Nonconvex Type

Abstract: In this paper we deal with the following singular perturbation problem: let $u^\e=u^\e(x,t)$ be the entropy solution of
\e(u_t+f(u)_x)=g(u), u(x,0)=u_0(x)
where $u_0$ is a given initial datum, the problem being to determine what happens to the family of solutions $u^\e$ as $\e\to 0^+$. By appropriate construction of traveling wave solution and by use of comparison principle, the limit is characterized in the case of a reaction term $g$ of bistable type, and for nonconvex flux $f$. This result generalize the previous one (for the convex case) proved by Fan, Jin and Teng (number 1998-37 in this server).

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