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1998 Nonnegative weak solutions of a porous medium equation with strong absorption
Chung-Ki Cho
Differential Integral Equations 11(6): 847-874 (1998).

Abstract

This paper studies the nonnegative weak solutions of a porous medium equation with strong absorption. We prove an apriori $\text{L}^{\infty}$ estimate through Moser iteration and obtain a compactness theorem and an integral-type Harnack inequality. Using these fundamental results we prove the existence of initial traces of weak solutions and obtain the existence of a fundamental solution and the nonexistence of a very singular solution, as byproducts. As an another application of our apriori estimates we prove the finiteness of the propagation speed without using comparison principle

Citation

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Chung-Ki Cho. "Nonnegative weak solutions of a porous medium equation with strong absorption." Differential Integral Equations 11 (6) 847 - 874, 1998.

Information

Published: 1998
First available in Project Euclid: 30 April 2013

zbMATH: 1014.35046
MathSciNet: MR1659260

Subjects:
Primary: 35K65
Secondary: 35Dxx, 35R35, 76S05

Rights: Copyright © 1998 Khayyam Publishing, Inc.

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Vol.11 • No. 6 • 1998
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