Asymptotic behaviors for nonlinear dispersive equations with damping or dissipative terms
Li, Ze1 ; Zhao, Lifeng2
1 Institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 10019 China
2 Wu Wen-Tsun Key Laboratory of Mathematics Chinese Academy of Science and Department of Mathematics University of Science and Technology of China Hefei 230026 Anhui China
Séminaire Laurent Schwartz — EDP et applications (2017-2018), Exposé no. 6, 11 p.

In this note, we will review our recent work on the asymptotic behaviors of nonlinear Klein-Gordon equation with damping terms and Landau-Lifschitz flows from Eucliedean spaces and hyperbolic spaces. By the method of concentration-compactness attractors, we prove that the global bounded solution will decouple into a finite number of equilibrium points with different shifts from the origin. For the Landau-Lifschitz flow from Euclidean spaces, we prove that the solution with energy below 4π will converge to some constant map in the energy space. While for the Landau-Lifschitz flow from two dimensional spaces, the solution will converge to some harmonic map.

Publié le :
DOI : 10.5802/slsedp.120
Li, Ze 1 ; Zhao, Lifeng 2

1 Institute of Mathematics Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing 10019 China
2 Wu Wen-Tsun Key Laboratory of Mathematics Chinese Academy of Science and Department of Mathematics University of Science and Technology of China Hefei 230026 Anhui China 
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Li, Ze; Zhao, Lifeng. Asymptotic behaviors for nonlinear dispersive equations with damping or dissipative terms. Séminaire Laurent Schwartz — EDP et applications (2017-2018), Exposé no. 6, 11 p. doi : 10.5802/slsedp.120. http://www.numdam.org/articles/10.5802/slsedp.120/

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