The Cauchy problem for heat equation with fractional Laplacian and exponential nonlinearity

Ahmad Z. Fino; Mokhtar Kirane

doi:10.3934/cpaa.2020160

Article Contents

2020, Volume 19, Issue 7: 3625-3650. Doi: 10.3934/cpaa.2020160

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The Cauchy problem for heat equation with fractional Laplacian and exponential nonlinearity

Ahmad Z. Fino^1, , and
Mokhtar Kirane^2,

1.
LaMA-Liban, Lebanese University, Faculty of Sciences, Department of Mathematics, P.O. Box 37 Tripoli, Lebanon
2.
LaSIE, Pôle Sciences et Technologies, Université de La Rochelle, Avenue Michel Crépeau, 17031 La Rochelle, France

^*Corresponding author
^*Corresponding author

Received: July 2019

Revised: January 2020

Published: April 2020

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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.

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Mathematics Subject Classification: Primary: 35K05, 46E30, 35A01; Secondary: 35B40, 26A33, 35K55.

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References

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