On the one model of the reaction-diffusion-advection type for the nonlinear equation of the heat and mass transfer №2

The present paper is aimed to the investigating of the multidimensional thermal structures in nonlinear incompressible dissipative media with the application of the latest scientific achievements in the asymptotic analysis. The class of the singularly perturbed multidimensional problems of nonlinear heat conduction, to which the asymptotic methods are applicable, has been singled out. We propose the reasonable algorithms for constructing the zero-order asymptotic solutions of the boundary layer type and the zero-order asymptotic solutions of the contrast structures type that describe the thermal structures in nonlinear homogeneous dissipative media. The use of an effective algorithm allows us to select and describe the transition surface in the neighborhood of which the internal layer of the contrast structure is localized. This approach extends to a more complex, so-called, critical case. The results of the paper are interpreted and illustrated by the example of a two-dimensional boundary value problem. They can be used to create a numerical algorithm that uses asymptotic analysis to construct spatially inhomogeneous mashes when describing the internal layer of contrast structure, and also for the purpose of constructing the test examples.