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arXiv · 1905.07787

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

Ahmad Fino·Mokhtar Kirane
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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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Ahmad Fino, Mokhtar Kirane. 2019-05-19. The Cauchy problem for heat equation with fractional Laplacian and exponential nonlinearity. https://arxiv.org/abs/1905.07787

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