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arXiv · 2601.15618

Existence and uniqueness of $L^1$-solutions to time-fractional nonlinear diffusion equations

Mikiya Kametaka·Tatsuki Kawakami
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Abstract

We establish the global existence and uniqueness of $L^1$-solutions to the Cauchy problem for time-fractional porous medium type nonlinear diffusion equations. Furthermore, we give the mass conservation law for $L^1$-solutions to time-fractional fast diffusion equations, and prove that the finite-time extinction does not occur for any nonnegative $L^1$-solutions.

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Mikiya Kametaka, Tatsuki Kawakami. 2026-01-22. Existence and uniqueness of $L^1$-solutions to time-fractional nonlinear diffusion equations. https://arxiv.org/abs/2601.15618

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