Singular perturbation in a nonlocal diffusion problem

LEDERMAN, CLAUDIA; WOLANSKI, NOEMÍ

COMMUNICATIONS IN PARTIAL DIFFERENTIAL EQUATIONS

Taylor & Francis

Lugar: Filadelfia; Año: 2006 vol. 31 p. 195 - 241

0360-5302

We study a singular perturbation problem for a nonlocal evolution operator. The problem appears in the analysis of the propagation of flames in the high activation energy limit, when admitting nonlocal effects. We obtain uniform estimates and we show that limits are solutions to a free boundary problem in a viscosity sense and in a pointwise sense at regular free boundary points. We study the nonlocal problem both for a single equation and for a  system of two equations. Some of the results obtained are new even when the operator under consideration is the heat operator.