Asymptotics of solutions and numerical simulation of the nonlinear heat conductivity problem with absorption and variable density

In the present work, the asymptotic behavior of the solutions of the nonlinear variable-density thermal conductivity problem with absorption is obtained. The critical value parameter is considered. The resulting asymptotics was used as an initial approximation, numerical calculations were performed. As a difference scheme, a three-layer difference scheme was used, which, unlike a two-layer scheme, has greater accuracy.