Well-posedness of initial-boundary value problem for time-fractional diffusion-wave equation with time-dependent coefficients
Analysis of PDEs
2025-05-23 v2
Abstract
We consider the well-posedness of the initial-boundary value problem for a time-fractional partial differential equation with the fractional order lying in (1,2]. For the case of time-dependent coefficients, it is difficult to give an explicit solution formula by the eigenfunction expansion method. In order to deal with the case of time-varying coefficients, we first show the unique existence and regularity of solution to a system of time-fractional ordinary differential equations. Then the unique existence of the weak solution to the time-fractional partial differential equation and improved regularity are derived by using the Galerkin method.
Cite
@article{arxiv.2203.10448,
title = {Well-posedness of initial-boundary value problem for time-fractional diffusion-wave equation with time-dependent coefficients},
author = {Xinchi Huang and Masahiro Yamamoto},
journal= {arXiv preprint arXiv:2203.10448},
year = {2025}
}