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Abstract: In this lecture, we study asymptotic behaviors of global and bounded solutions of gradient differential systems and discuss how to derive the long-time convergence of solutions by “gradient inequalities”. The idea that gradient inequalities force convergence of solutions of gradient systems was known to Lojasiewicz, who derived his celebrated gradient inequality for analytic gradient maps on finite-dimensional spaces. Simon proved infinite-dimensional gradient inequalities for analytic gradient maps associated with variational problems. The techniques developed by Lojasiewicz and Simon have been improved and applied to many problems. 

Seminar website:  Learning Seminar on PDE and Applications

( https://sites.math.rutgers.edu/~yyli/Learningseminar.html)