Asymptotic behaviors for nonlinear dispersive equations with damping or dissipative terms

Ze Li; Lifeng Zhao

doi:10.5802/slsedp.120

Ze Li ¹; Lifeng Zhao 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

Séminaire Laurent Schwartz — EDP et applications (2017-2018), Talk no. 6, 11 p.

Abstract

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 $4 π$ 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.

Published online: 2018-10-29

DOI: 10.5802/slsedp.120

Author's affiliations:

Ze Li ¹; Lifeng Zhao ²

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Ze Li; Lifeng Zhao. Asymptotic behaviors for nonlinear dispersive equations with damping or dissipative terms. Séminaire Laurent Schwartz — EDP et applications (2017-2018), Talk no. 6, 11 p. doi : 10.5802/slsedp.120. https://proceedings.centre-mersenne.org/articles/10.5802/slsedp.120/

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