Evolution of spatially localized thermal perturbations

The article considers a one-dimensional boundary problem of the nonlinear heat conduction equation in a two-dimensional layer filled with a medium with bulk heat absorption. Numerical solutions to this problem for different characteristic values, while using a standard difference scheme, confirm the theoretical conclusions about the propagation mode of thermal perturbations. Thermal perturbations from the heated walls prove to propagate through the nonlinear medium with bulk heat absorption at the finite rate of the front propagation. An effect of spatial localization of thermal perturbations, which can even reach the finite depth for nonterminating time, is also observed at the defined values of the problem characteristics.

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