Existence of solutions for a higher-order semilinear parabolic equation with singular initial data

Kazuhiro Ishige; Tatsuki Kawakami; Shinya Okabe

doi:10.1016/j.anihpc.2020.04.002

Existence of solutions for a higher-order semilinear parabolic equation with singular initial data

Kazuhiro Ishige, Tatsuki Kawakami, Shinya Okabe

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

Abstract

We establish the existence of solutions of the Cauchy problem for a higher-order semilinear parabolic equation by introducing a new majorizing kernel. We also study necessary conditions on the initial data for the existence of local-in-time solutions and identify the strongest singularity of the initial data for the solvability of the Cauchy problem.

Original language	English
Pages (from-to)	1185-1209
Number of pages	25
Journal	Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire
Volume	37
Issue number	5
DOIs	https://doi.org/10.1016/j.anihpc.2020.04.002
Publication status	Published - 2020 Sep 1
Externally published	Yes

Keywords

Higher-order semilinear parabolic equation
Majorizing kernel
Singular initial data
Solvability

ASJC Scopus subject areas

Analysis
Mathematical Physics
Applied Mathematics

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10.1016/j.anihpc.2020.04.002

Cite this

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title = "Existence of solutions for a higher-order semilinear parabolic equation with singular initial data",

abstract = "We establish the existence of solutions of the Cauchy problem for a higher-order semilinear parabolic equation by introducing a new majorizing kernel. We also study necessary conditions on the initial data for the existence of local-in-time solutions and identify the strongest singularity of the initial data for the solvability of the Cauchy problem.",

keywords = "Higher-order semilinear parabolic equation, Majorizing kernel, Singular initial data, Solvability",

author = "Kazuhiro Ishige and Tatsuki Kawakami and Shinya Okabe",

note = "Funding Information: The authors would like to thank the referees for their careful readings and useful comments. The authors of this paper were supported in part by the Grant-in-Aid for Scientific Research (S) (No. 19H05599 ), from Japan Society for the Promotion of Science . The second author was also supported in part by the Grant-in-Aid for Young Scientists (B) (No. 16K17629 ) from Japan Society for the Promotion of Science . Publisher Copyright: {\textcopyright} 2020 Elsevier Masson SAS",

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doi = "10.1016/j.anihpc.2020.04.002",

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T1 - Existence of solutions for a higher-order semilinear parabolic equation with singular initial data

AU - Ishige, Kazuhiro

AU - Kawakami, Tatsuki

AU - Okabe, Shinya

N1 - Funding Information: The authors would like to thank the referees for their careful readings and useful comments. The authors of this paper were supported in part by the Grant-in-Aid for Scientific Research (S) (No. 19H05599 ), from Japan Society for the Promotion of Science . The second author was also supported in part by the Grant-in-Aid for Young Scientists (B) (No. 16K17629 ) from Japan Society for the Promotion of Science . Publisher Copyright: © 2020 Elsevier Masson SAS

PY - 2020/9/1

Y1 - 2020/9/1

N2 - We establish the existence of solutions of the Cauchy problem for a higher-order semilinear parabolic equation by introducing a new majorizing kernel. We also study necessary conditions on the initial data for the existence of local-in-time solutions and identify the strongest singularity of the initial data for the solvability of the Cauchy problem.

AB - We establish the existence of solutions of the Cauchy problem for a higher-order semilinear parabolic equation by introducing a new majorizing kernel. We also study necessary conditions on the initial data for the existence of local-in-time solutions and identify the strongest singularity of the initial data for the solvability of the Cauchy problem.

KW - Higher-order semilinear parabolic equation

KW - Majorizing kernel

KW - Singular initial data

KW - Solvability

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JO - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

JF - Annales de l'Institut Henri Poincare. Annales: Analyse Non Lineaire/Nonlinear Analysis

SN - 0294-1449

IS - 5

ER -

Existence of solutions for a higher-order semilinear parabolic equation with singular initial data

Abstract

Keywords

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