In this paper we are consider a problem of nonlinear heat conduction with double nonlinearity under action of a strong absorption. For which an exact analytical solution is found, analysis of which makes it possible to reveal a number of 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.
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