Initial-boundary value problems for coupled systems of time-fractional diffusion equations

Abstract

This article deals with the initial-boundary value problem for a moderately coupled system of time-fractional diffusion equations. Defining the mild solution, we establish fundamental unique existence, limited smoothing property and long-time asymptotic behavior of the solution, which mostly inherit those of a single equation. Owing to the coupling effect, we also obtain the uniqueness for an inverse problem on determining all the fractional orders by the single point observation of a single component of the solution.

24 pages

References in corpus (5)

• Inverse Problems of Determining Sources of the Fractional Partial Differential Equations
• Inverse Problems of Determining Parameters of the Fractional Partial Differential Equations
• Inverse Problems of Determining Coefficients of the Fractional Partial Differential Equations
• Uniqueness of orders and parameters in multi-term time-fractional diffusion equations by short-time behavior
• Determining damping terms in fractional wave equations

Cited by in corpus (5)

• Forward and backward problems for coupled subdiffusion systems
• Long-time asymptotic estimate and a related inverse source problem for time-fractional wave equations
• Sharp decay estimates and numerical analysis for weakly coupled systems of two subdiffusion equations
• Numerical reconstruction of orders in coupled systems of subdiffusion equations
• Inverse $t$-source problem and a strict positivity property for coupled subdiffusion systems