Ukrainian Mathematical Bulletin

Volume 1, Issue 1, 2004 pp. 1-23.

The Cauchy Problem for Degenerate Parabolic Equations with Source and Damping

Authors: Daniele Andreucci, Anatoli F. Tedeev and Maura Ughi
Author institution: Universit`a La Sapienza, Italy, Inst. Applied Mathematics and Mechanics, National Academy of Sciences of Ukraine, Universit`a di Trieste Piazzale Europa, Italy

Summary: We prove optimal estimates for the decay of mass of solutions to the Cauchy problem for a wide class of quasilinear parabolic equations with damping terms. In the degenerate case, we also prove estimates for the finite speed of propagation. When the equation contains also a blow up term, we discuss existence and nonexistence of global solutions.

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