The Cauchy problem for heat equations with exponential nonlinearity

Norisuke Ioku

doi:10.1016/j.jde.2011.02.015

The Cauchy problem for heat equations with exponential nonlinearity

Norisuke Ioku

SCI - Mathematics

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

40 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 language	English
Pages (from-to)	1172-1194
Number of pages	23
Journal	Journal of Differential Equations
Volume	251
Issue number	4-5
DOIs	https://doi.org/10.1016/j.jde.2011.02.015
Publication status	Published - 2011 Aug 15

Keywords

Cauchy problems
Critical Sobolev embeddings
Global existence
Orlicz spaces

ASJC Scopus subject areas

Analysis
Applied Mathematics

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10.1016/j.jde.2011.02.015

Cite this

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title = "The Cauchy problem for heat equations with exponential nonlinearity",

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).",

keywords = "Cauchy problems, Critical Sobolev embeddings, Global existence, Orlicz spaces",

author = "Norisuke Ioku",

note = "Funding Information: The author would like to express his gratitude to Professor Takayoshi Ogawa for valuable advice and continuous encouragement. He also expresses his sincere thanks to Professor Michinori Ishiwata for his helpful comment. He is grateful to the referees for their helpful comments on the paper. This work was partially supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.",

year = "2011",

month = aug,

day = "15",

doi = "10.1016/j.jde.2011.02.015",

language = "English",

volume = "251",

pages = "1172--1194",

journal = "Journal of Differential Equations",

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publisher = "Academic Press Inc.",

number = "4-5",

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TY - JOUR

T1 - The Cauchy problem for heat equations with exponential nonlinearity

AU - Ioku, Norisuke

N1 - Funding Information: The author would like to express his gratitude to Professor Takayoshi Ogawa for valuable advice and continuous encouragement. He also expresses his sincere thanks to Professor Michinori Ishiwata for his helpful comment. He is grateful to the referees for their helpful comments on the paper. This work was partially supported by Research Fellowships of the Japan Society for the Promotion of Science for Young Scientists.

PY - 2011/8/15

Y1 - 2011/8/15

N2 - 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).

AB - 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).

KW - Cauchy problems

KW - Critical Sobolev embeddings

KW - Global existence

KW - Orlicz spaces

UR - http://www.scopus.com/inward/record.url?scp=79958189857&partnerID=8YFLogxK

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U2 - 10.1016/j.jde.2011.02.015

DO - 10.1016/j.jde.2011.02.015

M3 - Article

AN - SCOPUS:79958189857

VL - 251

SP - 1172

EP - 1194

JO - Journal of Differential Equations

JF - Journal of Differential Equations

SN - 0022-0396

IS - 4-5

ER -

The Cauchy problem for heat equations with exponential nonlinearity

Abstract

Keywords

ASJC Scopus subject areas

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