Unique continuation property for multi-terms time fractional diffusion equations

DOI10.1007/s00208-018-1710-zzbMath1420.35054arXiv1710.02384OpenAlexW2963397125WikidataQ129607580 ScholiaQ129607580MaRDI QIDQ2419946

Ching-Lung Lin, Gen Nakamura

Publication date: 4 June 2019

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1710.02384

zbMATH Keywords

Carleman estimateHolmgren-type transformation

Mathematics Subject Classification ID

Continuation and prolongation of solutions to PDEs (35B60) Fractional partial differential equations (35R11) Inequalities applied to PDEs involving derivatives, differential and integral operators, or integrals (35A23)

Related Items

Existence of mild solutions for Hilfer fractional evolution equations in Banach space, Optimal control of nonlocal fractional evolution equations in the \(\alpha\)-norm of order \((1,2)\), Uniqueness for an inverse coefficient problem for a one-dimensional time-fractional diffusion equation with non-zero boundary conditions, Uniqueness of solution with zero boundary condition for time-fractional wave equations, A fractional-order quasi-reversibility method to a backward problem for the multi-term time-fractional diffusion equation, Cauchy problems for Hilfer fractional evolution equations on an infinite interval, Cauchy problems of nonlinear nonautonomous fractional evolution equations, Inverse source problem for a one-dimensional time-fractional diffusion equation and unique continuation for weak solutions, Classical unique continuation property for multi-term time-fractional evolution equations, Well-posedness and regularity for fractional damped wave equations, New results on controllability of fractional evolution systems with order \(\alpha\in (1,2)\), Simultaneous inversion of the potential term and the fractional orders in a multi-term time-fractional diffusion equation

Cites Work

• Unnamed Item
• Solution for a fractional diffusion-wave equation defined in a bounded domain
• Cauchy problem for fractional diffusion equations
• Unique continuation property for the anomalous diffusion and its application
• Simultaneous inversion for the space-dependent diffusion coefficient and the fractional order in the time-fractional diffusion equation
• Coefficient inverse problem for a fractional diffusion equation
• Inverse source problem for a fractional diffusion equation
• Carleman estimate for a fractional diffusion equation with half order and application
• Conditional stability in determining a zeroth-order coefficient in a half-order fractional diffusion equation by a Carleman estimate
• Unique continuation property for anomalous slow diffusion equation
• Multi–dimensional solutions of space–time–fractional diffusion equations
• A Link Between Solvability of Pseudodifferential Equations and Uniqueness in the Cauchy Problem
• A tutorial on inverse problems for anomalous diffusion processes
• Spectral analysis of fractional kinetic equations with random data.
• The random walk's guide to anomalous diffusion: A fractional dynamics approach