A Comparison Theorem for a Nonlinear system Arising in Porous Medium Combustion

Abstract

Comparison theorems for the initial value finite domain one dimensional heat equation with a discontinuous forcing term are extended to a coupled system of a heat equation and an ordinary differential equation in space, rather than the usual ordinary differential equation in time, that arises in combustion theory.

Keywords:

• Coupled hyperbolic/parabolic differential equations
• discontinuous nonlinearity
• comparison theory