To asymptotic of the solution of the heat conduction problem with double nonlinearity, variable density, absorption at a critical parameter

Abstract

In this work we have established asymptotic behavior (for t →∞) of solutions of the Cauchy problem for a nonlinear heat equation with variable density describing the diffusion of heat with nonlinear heat absorption at the critical exponent of the parameter β. For numerical computations as an initial approximation we used founded the long time asymptotic of the solution. Numerical experiments and visualization were carried for one and two dimensional case.