Local existence and nonexistence of solutions to the Hardy parabolic equation with general nonlinearity

Yo Tsusaka

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arXiv · 2601.22520

Local existence and nonexistence of solutions to the Hardy parabolic equation with general nonlinearity

Yo Tsusaka

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Abstract

In this paper, we consider the Cauchy problem for the Hardy parabolic equation with general nonlinearity and establish the local existence and nonexistence results. Our results provide the optimal integrability conditions on initial function for the existence of a local-in-time nonnegative solution. The proof of the existence result is based on the supersolution method.

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Yo Tsusaka. 2026-01-30. Local existence and nonexistence of solutions to the Hardy parabolic equation with general nonlinearity. https://arxiv.org/abs/2601.22520

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