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Conditions for the time global existence and nonexistence of a compact support of solutions to the Cauchy problem for quasilinear degenerate parabolic equations

A. F. Tedeev

Institute of Applied Mathematics and Mechanics, Ukraine National Academy of Sciences

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.

Keywords: quasilinear degenerate parabolic equation, nonhomogeneous density, blow-up.

UDC: 517.946

Received: 17.05.2002

 English version: Siberian Mathematical Journal, 2004, 45:1, 155–164

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