Decay estimates for the time-fractional evolution equations with time-dependent coefficients

TL;DR

This paper derives optimal decay estimates for solutions to time-fractional evolution equations with both linear and nonlinear operators, including applications to biological and porous medium models.

Contribution

It provides new decay rate results for a range of time-fractional equations with nonlinear operators, extending existing theory.

Findings

Optimal decay rates for linear time-fractional equations

Decay estimates for nonlinear operators like p-Laplacian and porous medium

Applications to Fisher-KPP and porous medium equations

Abstract

In this paper, the initial-boundary value problems for the time-fractional degenerate evolution equations are considered. Firstly, in the linear case, we obtain the optimal rates of decay estimates of the solutions. The decay estimates are also established for the time-fractional evolution equations with nonlinear operators such as: p-Laplacian, the porous medium operator, degenerate operator, mean curvature operator, and Kirchhoff operator. At the end, some applications of the obtained results are given to derive the decay estimates of global solutions for the time-fractional Fisher-KPP-type equation and the time-fractional porous medium equation with the nonlinear source.