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

28 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

Access to Document

10.1016/j.jde.2011.02.015

Fingerprint Dive into the research topics of 'The Cauchy problem for heat equations with exponential nonlinearity'. Together they form a unique fingerprint.

Cite this

Ioku, N. (2011). The Cauchy problem for heat equations with exponential nonlinearity. Journal of Differential Equations, 251(4-5), 1172-1194. https://doi.org/10.1016/j.jde.2011.02.015

@article{b7a66911e1434b97b191a179ab1b9636,

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",

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",

issn = "0022-0396",

publisher = "Academic Press Inc.",

number = "4-5",

}

TY - JOUR

T1 - The Cauchy problem for heat equations with exponential nonlinearity

AU - Ioku, Norisuke

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

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

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 -