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Full paper in PDF:
$%P. Bénilan and M. Maliki, Approximation de la solution de viscosité d’un problème
d’Hamilton-Jacobi, Rev. Mat. Univ. Complut. Madrid 9 (1996), no. 2, 369–383.%$
We consider the Cauchy problem for a parabolic equation
, where
is a “small enough” non negative
continuous function; we prove uniform estimate of the modulus of continuity of
a classical solution
, existence of viscosity solutions
, and convergence, as
in appropriate sense, of these solutions to the viscosity solution of the
Cauchy problem for
.
1991 Mathematics Subject Classification: 35K65, 35B25, 35B65.