On the behavior of solutions to the Cauchy problem for a degenerate parabolic equation with inhomogeneous density and a source
А. В. МартыненкоInstitute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, ul. R. Lyuksemburg 74, Donetsk, 340114, UkraineAnatoli F. TedeevInstitute of Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, ul. R. Lyuksemburg 74, Donetsk, 340114, Ukraine
2008en
ABI
Abstract
The Cauchy problem for a degenerate parabolic equation with a source and inhomogeneous density of the form $$ \rho (x)\frac{{\partial u}} {{\partial t}} = div(u^{m - 1} \left| {Du} \right|^{\lambda - 1} Du) + \rho (x)u^p $$ 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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