Local classical solutions for a chemical system with free boundary

Abstract

This paper treats a two-dimensional, free-boundary problem arising in a mathematical model of chemical attack. A diffusion system is solved with a nonlinear condition on the free boundary, whose velocity is governed by the reaction of the concentrations of several compounds. An existence and uniqueness result of classical solutions is given in Hölder spaces, locally in time, for the corresponding Stefan-like problem to a system of parabolic equations with kinetic boundary condition.