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

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  • 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.

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


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