Initial-boundary value problems for coupled systems of time-fractional diffusion equations
Zhiyuan Li, Xinchi Huang, Yikan Liu
Abstract
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.
Topics & Concepts
MathematicsUniquenessBoundary value problemSmoothingMathematical analysisDiffusionComponent (thermodynamics)Diffusion equationApplied mathematicsPhysicsEconomicsThermodynamicsService (business)EconomyStatisticsFractional Differential Equations SolutionsNonlinear Differential Equations AnalysisDifferential Equations and Numerical Methods