Local well-posedness for the cauchy problem to nonlinear heat equations of Fujita type in nearly critical Besov space

Takayoshi Ogawa, Yuuki Yamane

Research output: Chapter in Book/Report/Conference proceedingConference contribution

1 Citation (Scopus)

Abstract

We show the local well-posedness of the Cauchy problem to a nonlinear heat equation of Fujita type in lower space dimensions. It is well known that the nonnegative solution corresponding to the Fujita critical exponent p=1+2/n does not exist in the critical scaling invariant space L1(Rn). We show if the initial data is in a modified Besov spaces, then the corresponding mild solution to the equation with the Fujita critical exponent p=1+2//n exists and the problem is locally well-posed in the same space of the initial data. Besides we also show the problem is ill-posed in the scaling invariant Besov and inhomogeneous Besov spaces. This is known in L1 space and extension of the result known in the Lebesgue spaces.

Original languageEnglish
Title of host publicationMathematics for Nonlinear Phenomena—Analysis and Computation - In Honor of Yoshikazu Giga’s 60th Birthday
EditorsYasunori Maekawa, Shuichi Jimbo
PublisherSpringer New York LLC
Pages215-239
Number of pages25
ISBN (Print)9783319667621
DOIs
Publication statusPublished - 2017
EventInternational Conference on Mathematics for Nonlinear Phenomena: Analysis and Computation in Honor of Professor Yoshikazu Giga on his 60th Birthday, MNP 2015 - Sapporo, Japan
Duration: 2015 Aug 162015 Aug 18

Publication series

NameSpringer Proceedings in Mathematics and Statistics
Volume215
ISSN (Print)2194-1009
ISSN (Electronic)2194-1017

Other

OtherInternational Conference on Mathematics for Nonlinear Phenomena: Analysis and Computation in Honor of Professor Yoshikazu Giga on his 60th Birthday, MNP 2015
Country/TerritoryJapan
CitySapporo
Period15/8/1615/8/18

Keywords

  • Fujita critical exponent
  • Local well-posedness
  • Modified Besov space
  • Nonlinear heat equation

ASJC Scopus subject areas

  • Mathematics(all)

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