About new nonlinear properties of the problem of nonlinear thermal conductivity
Keywords:degenerate nonlinear, estimate, exact solution, localization, parabolic equation
In this paper we consider a problem of nonlinear heat conduction with double nonlinearity under the action of strong absorption. For which an exact analytical solution is found, analysis of which makes it possible to reveal several characteristic features of thermal processes in nonlinear media. The following nonlinear effects are established: an inertial effect of a finite velocity of propagation of thermal disturbances, spatial heat localization, and finite time effect i.e. existence of a thermal structure in a medium with strong absorption. The following nonlinear effects are observed in the problem under consideration: the inertial effect of an ultimate speed of propagation of thermal perturbations, the effect of spatial localization of heat, and the effect of ultimate time of the thermal structure in an absorption medium.
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