On the behavior of solutions to the Cauchy problem for a degenerate parabolic equation with inhomogeneous density and a source

A. V. Martynenko   ; A. F. Tedeev

Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 7, pp. 1214-1229

Résumé

The Cauchy problem for a degenerate parabolic equation with a source and inhomogeneous density of the form $$ \rho(x)\frac{\partial u}{\partial t}=\operatorname{div}(u^{m-1}|Du|^{\lambda-1}Du)+\rho(x)u^p. $$ is studied. Time global existence and nonexistence conditions are found for a solution to the Cauchy problem. Exact estimates of the solution are obtained in the case of global solvability.

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