The cauchy problem for heat equation with fractional laplacian and exponential nonlinearity

Ahmad Z. Fino; Mokhtar Kirane

doi:10.3934/CPAA.2020160

The cauchy problem for heat equation with fractional laplacian and exponential nonlinearity

Ahmad Z. Fino, Mokhtar Kirane

Mathematics

Lebanese University

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

10 Scopus citations

Abstract

We consider the Cauchy problem for heat equation with fractional Laplacian and exponential nonlinearity. We establish local well-posedness result in Orlicz spaces. We derive the existence of global solutions for small initial data. We obtain decay estimates for large time in Lebesgue spaces.

Original language	British English
Pages (from-to)	3625-3650
Number of pages	26
Journal	Communications on Pure and Applied Analysis
Volume	19
Issue number	7
DOIs	https://doi.org/10.3934/CPAA.2020160
State	Published - Jul 2020

Keywords

Decay estimates
Fractional Laplacian
Global existence
Orlicz spaces
Well-posedness

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10.3934/CPAA.2020160

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title = "The cauchy problem for heat equation with fractional laplacian and exponential nonlinearity",

abstract = "We consider the Cauchy problem for heat equation with fractional Laplacian and exponential nonlinearity. We establish local well-posedness result in Orlicz spaces. We derive the existence of global solutions for small initial data. We obtain decay estimates for large time in Lebesgue spaces.",

keywords = "Decay estimates, Fractional Laplacian, Global existence, Orlicz spaces, Well-posedness",

author = "Fino, {Ahmad Z.} and Mokhtar Kirane",

year = "2020",

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T1 - The cauchy problem for heat equation with fractional laplacian and exponential nonlinearity

AU - Fino, Ahmad Z.

AU - Kirane, Mokhtar

PY - 2020/7

Y1 - 2020/7

N2 - We consider the Cauchy problem for heat equation with fractional Laplacian and exponential nonlinearity. We establish local well-posedness result in Orlicz spaces. We derive the existence of global solutions for small initial data. We obtain decay estimates for large time in Lebesgue spaces.

AB - We consider the Cauchy problem for heat equation with fractional Laplacian and exponential nonlinearity. We establish local well-posedness result in Orlicz spaces. We derive the existence of global solutions for small initial data. We obtain decay estimates for large time in Lebesgue spaces.

KW - Decay estimates

KW - Fractional Laplacian

KW - Global existence

KW - Orlicz spaces

KW - Well-posedness

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U2 - 10.3934/CPAA.2020160

DO - 10.3934/CPAA.2020160

M3 - Article

AN - SCOPUS:85085325792

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EP - 3650

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 7

ER -

The cauchy problem for heat equation with fractional laplacian and exponential nonlinearity

Abstract

Keywords

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