Construction of Solutions to a Boundary Value Problem with Singularity for a Nonlinear Parabolic System

We consider a system of two nonlinear second-order parabolic equations with singularity. Systems of this type are applied in chemical kinetics to describe reaction-diffusion processes. We prove the existence and uniqueness theorem of an analytic solution having the diffusion-wave type at a given wave front. The proof is constructive, and the solution had the form of a power series with recursively calculated coefficients. Moreover, we propose some numerical algorithm based on the boundary element method whose verification uses the segments of analytic solutions.