Stabilization in degenerate parabolic equations in divergence form and application to chemotaxis systems

Sachiko Ishida and Tomomi Yokota

Address:
Department of Mathematics and Informatics, Graduate School of Science, Chiba University, 1-33, Yayoi-cho, Inage, Chiba 263-8522, Japan
Department of Mathematics, Tokyo University of Science, 1-3, Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan

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Abstract: This paper presents a stabilization result for weak solutions of degenerate parabolic equations in divergence form. More precisely, the result asserts that the global-in-time weak solution converges to the average of the initial data in some topology as time goes to infinity. It is also shown that the result can be applied to a degenerate parabolic-elliptic Keller-Segel system.

AMSclassification: primary 35B35; secondary 35D30, 35Q92, 92C17.

Keywords: stabilization, degenerate diffusion, Keller-Segel systems.

DOI: 10.5817/AM2023-2-181