Kink dynamics in the \phi^4 model: asymptotic stability for odd perturbations in the energy space
Automated Media Analysis
These types of automated video analysis does the TIB AVPortal use:
Scene recognition — shot boundary detection segments the video on the basis of image characteristics. A visual table of contents created from this provides a quick overview of the video content, facilitating accurate access.
Text recognition – intelligent character recognition determines and indexes written language (such as text written on slides), and makes it searchable.
Speech recognition – speech to text notes down spoken language in the video in the form of a transcript, which is searchable.
Image recognition – visual concept detection indexes the moving image using subjectspecific and multidisciplinary visual concepts (for example, landscape, façade detail, technical drawing, computer animation or lecture).
Indexing – namedentity recognition describes individual video segments with semantically associated terms. This ensures that synonyms or hyponyms of any search terms entered are also searched for automatically, increasing the number of hits.
Metadata
Formal Metadata
Title  Kink dynamics in the \phi^4 model: asymptotic stability for odd perturbations in the energy space 
Title of Series  Trimestre Ondes Non linéaires  June Conference 
Part Number  4 
Number of Parts  23 
Author 
Kowalcyk, Michal

License 
CC Attribution 3.0 Unported: You are free to use, adapt and copy, distribute and transmit the work or content in adapted or unchanged form for any legal purpose as long as the work is attributed to the author in the manner specified by the author or licensor. 
DOI  10.5446/20820 
Publisher  Institut des Hautes Études Scientifiques (IHÉS) 
Release Date  2016 
Language  English 
Content Metadata
Subject Area  Mathematics 
Abstract  Kink dynamics in the \phi^4 model: asymptotic stability for odd perturbations in the energy space We consider a classical equation \[\phi \phi =\phi\phi^3,\quad (t,x)\in\RR\times\RR\] known as the \phi^4 model in one space dimension. The kink, defined by H(x)=\tanh(x/}), is an explicit stationary solution of this model. From a result of Henry, Perez and Wreszinski it is known that the kink is orbitally stable with respect to small perturbations of the initial data in the energy space. In this paper we show asymptotic stability of the kink for odd perturbations in the energy space. The proof is based on Virialtype estimates partly inspired from previous works of Martel and Merle on asymptotic stability of solitons for the generalized Kortewegde Vries equations. However, this approach has to be adapted to additional difficulties, pointed out by Soffer and Weinstein in the case of general nonlinear KleinGordon equations with potential: the interactions of the socalled internal oscillation mode with the radiation, and the different rates of decay of these two components of the solution in large time. 