Asymptotic behavior of solutions of some semilinear heat equations in RN

Kazuhiro Ishige, Tatsuki Kawakamiy

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

We consider the Cauchy problem of the semilinear heat equa- tion, where N ≥ ∞, f ∇ C1([0,∞)), and Ф ∇ L1(RN) ∩ L∞(RN) satisfying some suitable conditions. We study the asymptotic behavior of the solutions in the Lq space for q ∇ [1,∞] by using the relative entropy methods.

Original languageEnglish
Title of host publicationRecent Advances in Nonlinear Analysis
PublisherWorld Scientific Publishing Co.
Pages171-180
Number of pages10
ISBN (Electronic)9789812709257
ISBN (Print)981270924X, 9789812709240
DOIs
Publication statusPublished - 2008 Jan 1

Keywords

  • Asymptotic behavior
  • Cauchy problem
  • Relative entropy methods
  • Semilinear heat equa-tion

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

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  • Cite this

    Ishige, K., & Kawakamiy, T. (2008). Asymptotic behavior of solutions of some semilinear heat equations in RN. In Recent Advances in Nonlinear Analysis (pp. 171-180). World Scientific Publishing Co.. https://doi.org/10.1142/9789812709257_00011