Electron. J. Differential Equations, Vol. 2021 (2021), No. 29, pp. 1-11.

Extinction in finite time of solutions to fractional parabolic porous medium equations with strong absorption

Nguyen Anh Dao

In this article we study the solutions of a general fractional parabolic porous medium equation with a non-Lipschitz absorption term. We obtain the existence of weak solutions, Lp-estimates, and decay estimates. Also, we show that weak solutions must vanish after a finite time, even for large initial data.

Submitted December 11, 2020. Published April 13, 2021.
Math Subject Classifications: 35R11, 35K65.
Key Words: Nonlocal nonlinear parabolic equation; fractional Laplacian; finite time extinction.

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Nguyen Anh Dao
Institute of Applied Mathematics
University of Economics
Ho Chi Minh City, Viet Nam
email: anhdn@ueh.edu.vn

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