Existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term

Kazuhiro Ishige; Tatsuki Kawakami; Ryo Takada

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arXiv · 2407.17769

Existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term

Kazuhiro Ishige·Tatsuki Kawakami·Ryo Takada

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Abstract

We study the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term. For this aim, we establish decay estimates of the fractional heat semigroup in several uniformly local Zygumnd spaces. Furthermore, we apply the real interpolation method in uniformly local Zygmund spaces to obtain sharp integral estimates on the inhomogeneous term and the nonlinear term. This enables us to find sharp sufficient conditions for the existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term.

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Kazuhiro Ishige, Tatsuki Kawakami, Ryo Takada. 2024-07-25. Existence of solutions to the fractional semilinear heat equation with a singular inhomogeneous term. https://arxiv.org/abs/2407.17769

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