Construction of solutions to the boundary value problem with singularity for a nonlinear parabolic system

The paper considers 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 the analytical solution having the diffusion-wave type at a given wave front. The proof is constructive, and the solution is constructed in the form of a power series with recursively calculated coefficients. Besides, we propose a numerical algorithm based on the boundary element method. For its verification, we use segments of analytical solutions.