Unique continuation property for anomalous slow diffusion equation

DOI10.1080/03605302.2015.1135164zbMath1350.35048arXiv1312.7639OpenAlexW2344363101MaRDI QIDQ3188114

Gen Nakamura, Ching-Lung Lin

Publication date: 16 August 2016

Published in: Communications in Partial Differential Equations (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1312.7639

zbMATH Keywords

anomalous diffusionCarleman estimatesubelliptic estimatesfractional time derivative

Mathematics Subject Classification ID

Second-order elliptic equations (35J15) Microlocal methods and methods of sheaf theory and homological algebra applied to PDEs (35A27) Continuation and prolongation of solutions to PDEs (35B60) Fractional partial differential equations (35R11)

Related Items (12)

Lipschitz stability estimates in inverse source problems for a fractional diffusion equation of half order in time by Carleman estimates ⋮ On time-fractional diffusion equations with space-dependent variable order ⋮ Hölder stability estimate in an inverse source problem for a first and half order time fractional diffusion equation ⋮ Uniqueness for an inverse coefficient problem for a one-dimensional time-fractional diffusion equation with non-zero boundary conditions ⋮ Unique continuation property for multi-terms time fractional diffusion equations ⋮ Uniqueness for fractional nonsymmetric diffusion equations and an application to an inverse source problem ⋮ 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 ⋮ Reconstruction of the temporal component in the source term of a (time-fractional) diffusion equation ⋮ Unique continuation principle for the one-dimensional time-fractional diffusion equation ⋮ Global Lipschitz stability for a fractional inverse transport problem by Carleman estimates

Cites Work

• 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
• 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
• Multi–dimensional solutions of space–time–fractional diffusion equations
• A Link Between Solvability of Pseudodifferential Equations and Uniqueness in the Cauchy Problem
• Spectral analysis of fractional kinetic equations with random data.
• The random walk's guide to anomalous diffusion: A fractional dynamics approach

This page was built for publication: Unique continuation property for anomalous slow diffusion equation