Geodesic
On the behavior of solutions to the Cauchy problem for a degenerate parabolic equation with inhomogeneous density and a source
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 7, pp. 1214-1229

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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. 
@article{ZVMMF_2008_48_7_a7,
     author = {A. V. Martynenko and A. F. Tedeev},
     title = {On the behavior of solutions to the {Cauchy} problem for a~degenerate parabolic equation with inhomogeneous density and a~source},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1214--1229},
     publisher = {mathdoc},
     volume = {48},
     number = {7},
     year = {2008},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_7_a7/}
}
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A. V. Martynenko; A. F. Tedeev. On the behavior of solutions to the Cauchy problem for a degenerate parabolic equation with inhomogeneous density and a source. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 7, pp. 1214-1229. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_7_a7/