Classification of connecting solutions of semilinear parabolic equations
Analysis of PDEs
2007-09-18 v1
Abstract
For a given semilinear parabolic equation with polynomial nonlinearity, many solutions blow up in finite time. For a certain large class of these equations, we show that some of the solutions which do not blow up actually tend to equilibria. The characterizing property of such solutions is a finite energy constraint, which comes about from the fact that this class of equations can be written as the gradient of a certain functional.
Keywords
Cite
@article{arxiv.0709.2705,
title = {Classification of connecting solutions of semilinear parabolic equations},
author = {Michael Robinson},
journal= {arXiv preprint arXiv:0709.2705},
year = {2007}
}