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Convergence to Equilibria of Global Solutions to Quasilinear Keller--Segel Systems

江 杰(中国科学院武汉物理与数学研究所,副教授)
Monday, January 1st, 2018, 9:30 AM  华东师范大学

In this talk, we shall present some recent results on convergence of globally bounded solutions towards equilibria of certain quasilinear Keller-Segel models. First, for quasilinear Keller-Segel models with non-degenerate diffusions, with the help of a non-smooth version of Simon-Lojasiewicz inequality, we prove that if globally bounded solution exists, then it must converge to an equilibrium. Then, we study the prototype degenerate case with a porous medium type diffusion term. By a new regularization, we prove the global existence of weak solutions together with an energy dissipation inequality. Then, we discuss the convergence property by a modified Simon-Lojasiwicz inequality.

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