Threshold and strong threshold solutions of a semilinear parabolic equation

Pavol Quittner

Threshold and strong threshold solutions of a semilinear parabolic equation

Analysis of PDEs 2016-05-25 v1

Authors: Pavol Quittner

Abstract

If $p>1+2/n$ then the equation $u_t-\Delta u = u^p, \quad x\in{\mathbb R}^n,\ t>0,$ possesses both positive global solutions and positive solutions which blow up in finite time. We study the large time behavior of radial positive solutions lying on the borderline between global existence and blow-up.

Keywords

semilinear parabolic equation threshold solutions blow-up global existence radial solutions large time behavior

Cite

@article{arxiv.1605.07388,
  title  = {Threshold and strong threshold solutions of a semilinear parabolic equation},
  author = {Pavol Quittner},
  journal= {arXiv preprint arXiv:1605.07388},
  year   = {2016}
}

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