Existence, Non-existence, and Uniqueness for a Heat Equation with Exponential Nonlinearity in ℝ2

Norisuke Ioku, Bernhard Ruf, Elide Terraneo

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

We consider a semilinear heat equation with exponential nonlinearity in ℝ2. We prove that local solutions do not exist for certain data in the Orlicz space exp L2(ℝ2), even though a small data global existence result holds in the same space exp L2(ℝ2). Moreover, some suitable subclass of exp L2(ℝ2) for local existence and uniqueness is proposed.

Original languageEnglish
Article number29
JournalMathematical Physics Analysis and Geometry
Volume18
Issue number1
DOIs
Publication statusPublished - 2015 Dec 1
Externally publishedYes

Keywords

  • Critical nonlinearity
  • Existence
  • Heat equation
  • Non-existence
  • Uniqueness

ASJC Scopus subject areas

  • Mathematical Physics
  • Geometry and Topology

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