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Bubbling location for $F$-harmonic maps and Inhomogeneous Landau-Lifshitz equations | Yuxiang Li
; Youde Wang
; | Date: |
25 Apr 2005 | Subject: | Analysis of PDEs; Mathematical Physics MSC-class: 35Q60;58E20 | math.AP math-ph math.MP | Abstract: | Let $f$ be a positive smooth function on a close Riemann surface (M,g). The $f-energy$ of a map $u$ from $M$ to a Riemannian manifold $(N,h)$ is defined as $$E_f(u)=int_Mf|
abla u|^2dV_g.$$ In this paper, we will study the blow-up properties of Palais-Smale sequences for $E_f$. We will show that, if a Palais-Smale sequence is not compact, then it must blows up at some critical points of $f$. As a sequence, if an inhomogeneous Landau-Lifshitz system, i.e. a solution of $$u_t=u imes au_f(u)+ au_f(u),u:M o S^2$$ blows up at time $infty$, then the blow-up points must be the critical points of $f$. | Source: | arXiv, math.AP/0504502 | Services: | Forum | Review | PDF | Favorites |
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