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
Chung-Ki Cho. "Nonnegative weak solutions of a porous medium equation with strong absorption." Differential Integral Equations 11 (6) 847 - 874, 1998. https://doi.org/10.57262/die/1367329480
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