The Cauchy problem for heat equations with exponential nonlinearity

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28 Citations (Scopus)

Abstract

The Cauchy problem for the semilinear heat equations is studied in the Orlicz space exp L 2(R{double-struck}n), where any power behavior of interaction works as a subcritical nonlinearity. We prove the existence of global solutions for the semilinear heat equations with the exponential nonlinearity under the smallness condition on the initial data in exp L2(R{double-struck}n).

Original languageEnglish
Pages (from-to)1172-1194
Number of pages23
JournalJournal of Differential Equations
Volume251
Issue number4-5
DOIs
Publication statusPublished - 2011 Aug 15

Keywords

  • Cauchy problems
  • Critical Sobolev embeddings
  • Global existence
  • Orlicz spaces

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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