Multidimensional singularly perturbed reaction-diffusion-advection problems with a balanced nonlinearity and their applications in the theory of nonlinear heat conductivity

Abstract

The stationary Lyapunov-stable solutions with internal transition layers (contrast structures) of multidimensional singularly perturbed reaction-diffusion-advection problems are investigated with the use of the modern methods of asymptotic analysis. On the basis of the modified boundary-function method, the asymptotic approximations of such solutions of an arbitrary order of accuracy in the case of a balanced nonlinearity are obtained. We propose a justified and effective algorithm that allows us to define and describe the localization region of the internal layer of contrast structure. We use this result to describe the thermal structures in the homogeneous nonlinear dissipative media.