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

TL;DR

This paper proves the existence and uniqueness of $L^1$-solutions for time-fractional nonlinear diffusion equations, including mass conservation and non-occurrence of finite-time extinction.

Contribution

It establishes the global existence and uniqueness of $L^1$-solutions for these equations, extending understanding of their behavior.

Findings

Proved global existence and uniqueness of $L^1$-solutions.

Established mass conservation law for $L^1$-solutions.

Showed finite-time extinction does not occur for nonnegative solutions.

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.