PDE Real Analysis Seminar

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Date, time & place Tuesday 10:30 - 11:30 056Room #056 (Graduate School of Math. Sci. Bldg.)

2012/12/05

10:30-11:30   Room #002 (Graduate School of Math. Sci. Bldg.)
Jie Jiang (Wuhan Institute of Physics and Mathematics, Chinese Academy of Sciences)
Convergence to Equilibrium of Bounded Solutions with Application of Lojasiewicz-Simon's inequality (ENGLISH)
[ Abstract ]
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.