The Cauchy problem for a combustion model in a porous medium with two layers (Q1757407)

The authors consider the Cauchy problem for a combustion model in a porous medium with two layers. The problem is spatially 1-dimensional (on the whole \(\mathbb R^1\)) and consists of reaction-diffusion equations and ordinary differential equations for fuel concentrations. The authors establish the local and the global (in time) existence of classical solutions for Lipschitz bounded non-negative initial distributions. Continuation to the global is under an additional assumptions that the initial distributions belong to some \(L_p\) and are smooth.