Abstract:
The Cauchy problem for a degenerate parabolic equation with a source and inhomogeneous density of the form
$$
\rho(x)\frac{\partial u}{\partial t}=\operatorname{div}(u^{m-1}|Du|^{\lambda-1}Du)+\rho(x)u^p.
$$
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.
Key words:equations with inhomogeneous density, degenerate parabolic equation, blowup solution, existence and nonexistence theorems.
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