Abstract
We study a quasilinear degenerate parabolic equation with a nonhomogeneous density. We establish that depending on the behavior of the density at infinity either a solution to the Cauchy problem possesses the property that the speed of propagation of perturbations is finite or the support blows up in finite time.
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Tedeev, A.F. Conditions for the Time Global Existence and Nonexistence of a Compact Support of Solutions to the Cauchy Problem for Quasilinear Degenerate Parabolic Equations. Siberian Mathematical Journal 45, 155–164 (2004). https://doi.org/10.1023/B:SIMJ.0000013021.66528.b6
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DOI: https://doi.org/10.1023/B:SIMJ.0000013021.66528.b6