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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)
2018-01-01 12:13  华东师范大学

江杰,中国科学院武汉物理与数学研究所副研究员,2009年于复旦大学数学科学学院获得理学博士学位,师从郑宋穆教授。2009年到2011年在北京应用物理与计算数学研究所在郭柏灵院士指导下从事博士后工作。主要针对多类非线性发展方程,如相场-流体方程组、趋化方程组等,考察整体解的存在唯一性、有界性、渐近性、平衡态以及无穷维动力系统的性质等,目前正式发表SCI论文14篇。

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.

主持人:张艳艳