Well-posedness of initial-boundary value problem for time-fractional diffusion-wave equation with time-dependent coefficients

2022/03/20 by Xinchi Huang, Masahiro Yamamoto, Huang, Xinchi +1 · 2 citations
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.2203.10448

openalex publication_date 2022/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Cited by

• Optimal Neumann boundary and distributed control of the Westervelt equation with time-fractional attenuation
• Inverse problem for the abstract diffusion-wave equation with Caputo fractional derivative

Related

• Decay rates and initial values for time-fractional diffusion-wave equations
• Simultaneous determination of initial value and source term for time-fractional wave-diffusion equations
• Well-posedness and asymptotic estimate for a diffusion equation with time-fractional derivative
• Well-posedness for weak and strong solutions of non-homogeneous initial boundary value problems for fractional diffusion equations
• Initial-boundary value problems for multi-term time-fractional diffusion equations with x-dependent coefficients