RMC - Vol. 9, Num. 2 - P. Bénilan/M. Maliki

Full paper in PDF:
$%P. Bénilan and M. Maliki, Approximation de la solution de viscosité d’un problème d’Hamilton-Jacobi, Rev. Mat. Univ. Complut. Madrid 9 (1996), no. 2, 369–383.%$

Approximation de la solution de viscosité d’un problème d’Hamilton-Jacobi

Philippe BÉNILAN and Mohamed MALIKI

Laboratoire de Mathématiques
URA CNRS 741
Université de Franche-Comté
Route de Gray 25030
Besançon cedex — France

Received: April 21, 1995

ABSTRACT

We consider the Cauchy problem for a parabolic equation $vt= oc (v)Dv+ | \~/ v| 2 +F (v)$ , where $oc (v)$ is a “small enough” non negative continuous function; we prove uniform estimate of the modulus of continuity of a classical solution $v$ , existence of viscosity solutions $v$ , and convergence, as $oc --> 0$ in appropriate sense, of these solutions to the viscosity solution of the Cauchy problem for $2 vt= | \~/ v |+ F(v)$ .

1991 Mathematics Subject Classification: 35K65, 35B25, 35B65.