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

Takayoshi Ogawa, Yuuki Yamane

研究成果: Conference contribution

1 被引用数 (Scopus)

抄録

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.

本文言語English
ホスト出版物のタイトルMathematics for Nonlinear Phenomena—Analysis and Computation - In Honor of Yoshikazu Giga’s 60th Birthday
編集者Yasunori Maekawa, Shuichi Jimbo
出版社Springer New York LLC
ページ215-239
ページ数25
ISBN(印刷版)9783319667621
DOI
出版ステータスPublished - 2017
イベントInternational Conference on Mathematics for Nonlinear Phenomena: Analysis and Computation in Honor of Professor Yoshikazu Giga on his 60th Birthday, MNP 2015 - Sapporo, Japan
継続期間: 2015 8 162015 8 18

出版物シリーズ

名前Springer Proceedings in Mathematics and Statistics
215
ISSN(印刷版)2194-1009
ISSN(電子版)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
国/地域Japan
CitySapporo
Period15/8/1615/8/18

ASJC Scopus subject areas

  • 数学 (全般)

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