Initial traces and solvability of the fast diffusion equation with power-type nonlinearity

Kazuhiro Ishige; Nobuhito Miyake

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arXiv · 2509.26054

Initial traces and solvability of the fast diffusion equation with power-type nonlinearity

Kazuhiro Ishige·Nobuhito Miyake

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Abstract

We investigate the qualitative behavior of the initial traces of nonnegative solutions to the fast diffusion equation with power-type nonlinearity. Necessary conditions for the existence of solutions to the corresponding Cauchy problem are identified. Moreover, sharp sufficient conditions for the existence of solutions are established by employing uniform local Morrey spaces and their generalizations.

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Kazuhiro Ishige, Nobuhito Miyake. 2025-09-30. Initial traces and solvability of the fast diffusion equation with power-type nonlinearity. https://arxiv.org/abs/2509.26054

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