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

Mikiya Kametaka; Tatsuki Kawakami

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

Analysis of PDEs 2026-05-20 v2

Authors: Mikiya Kametaka , Tatsuki Kawakami

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.

Keywords

time-fractional diffusion equations L^1-solutions Cauchy problem porous medium equation fast diffusion equation

Cite

@article{arxiv.2601.15618,
  title  = {Existence and uniqueness of $L^1$-solutions to time-fractional nonlinear diffusion equations},
  author = {Mikiya Kametaka and Tatsuki Kawakami},
  journal= {arXiv preprint arXiv:2601.15618},
  year   = {2026}
}

Comments

33 pages

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