Construction of a stable periodic solution to a semilinear heat equation with a prescribed profile
MetadataShow full item record
We construct a periodic solution to the semilinear heat equation with power nonlinearity, in one space dimension, which blows up in finite time T only at one blow-up point. We also give a sharp description of its blow-up profile. The proof relies on the reduction of the problem to a finite dimensional one and the use of index theory to conclude. Thanks to the geometrical interpretation of the finite-dimensional parameters in terms of the blow-up time and blow-up point, we derive the stability of the constructed solution with respect to initial data.
Artículo de publicación ISI
Fondecyt Grant, Fondo Basal CMM 1140311 Millennium Nucleus Center for Analysis of PDE NC130017 ERC, BLOWDISOL 291214 ANR project, ANAE ANR-13-BS01-0010-03
DOI: DOI: 10.1016/j.na.2015.09.002
Quote ItemNonlinear Analysis - Theory Methods & Applications Volumen: 131 Jan 2016
The following license files are associated with this item: