English

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 L2L^2 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}
}