Refined asymptotic expansions of solutions to fractional diffusion equations

TL;DR

This paper improves upon previous work by deriving higher order asymptotic expansions for the large time behavior of solutions to inhomogeneous and nonlinear fractional diffusion equations, enhancing understanding of their long-term dynamics.

Contribution

It provides refined asymptotic expansions for fractional diffusion equations, extending prior results with higher order terms for both linear and nonlinear cases.

Findings

Higher order asymptotic expansions derived

Enhanced understanding of long-term solution behavior

Improved approximation accuracy for large time solutions

Abstract

In this paper, as an improvement of the paper [K. Ishige, T. Kawakami and H. Michihisa, SIAM J. Math. Anal. 49 (2017) pp. 2167--2190], we obtain the higher order asymptotic expansions of the large time behavior of the solution to the Cauchy problem for inhomogeneous fractional diffusion equations and nonlinear fractional diffusion equations.