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THE CAUCHY PROBLEM FOR HEAT EQUATION WITH FRACTIONAL LAPLACIAN AND EXPONENTIAL NONLINEARITY
Journal article   Open access  Peer reviewed

THE CAUCHY PROBLEM FOR HEAT EQUATION WITH FRACTIONAL LAPLACIAN AND EXPONENTIAL NONLINEARITY

Ahmad Z. Fino, Mokhtar Kirane and LaSIE, Pôle Sciences et Technologies, Université de La Rochelle, Avenue Michel Crépeau, 17031 La Rochelle, France
Communications on pure and applied analysis, Vol.19(7), pp.3625-3650
01/07/2020
DOI: https://doi.org/10.3934/cpaa.2020160

Abstract

Mathematics Mathematics, Applied Physical Sciences Science & Technology
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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https://doi.org/10.3934/cpaa.2020160View
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