PDE seminar: Convergence to Equilibrium of Bounded Solutions with Application of Lojasiewicz-Simon’s inequality

Date
2013-1-7 16:30 - 2013-1-7 17:30
Place
Faculty of Science Building #3, Room 309
Speaker/Organizer
Jie Jiang (Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences )
 
In this talk, we present the application of Lojasiewicz
-Simon’s inequality to the study on convergence of
bounded global solutions to some evolution equations.
We take a semi-linear parabolic initial-boundary problem
as an example. With the help of Lojasiewicz
-Simon’s inequality we prove that the bounded global
solution will converge to an equilibrium as time goes to
infinity provided the nonlinear term is analytic in the
unknown function. We also present the application of
Lojasiewicz-Simon’s inequality to the asymptotic behavior
studies on phase-field models with Cattaneo
law and chemotaxis models with volume-filling effect.