Quantification of the unique continuation property for the heat equation

DOI10.3934/mcrf.2017012zbMath1366.35234OpenAlexW2730667981MaRDI QIDQ2360789

Laurent Bourgeois

Publication date: 12 July 2017

Published in: Mathematical Control and Related Fields (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3934/mcrf.2017012

zbMATH Keywords

heat equationdistance functionCarleman estimatestability estimatelateral Cauchy data

Mathematics Subject Classification ID

Heat equation (35K05) Ill-posed problems for PDEs (35R25) Inverse problems for PDEs (35R30)

Related Items (5)

Global logarithmic stability of a Cauchy problem for anisotropic wave equations ⋮ A stability estimate for data assimilation subject to the heat equation with initial datum ⋮ The unique continuation property for second order evolution PDEs ⋮ Global stability result for parabolic Cauchy problems ⋮ Stably determining time-dependent convection–diffusion coefficients from a partial Dirichlet-to-Neumann map

Cites Work

• Application of mixed formulations of quasi-reversibility to solve ill-posed problems for heat and wave equations: the 1D case
• Quantification of the unique continuation property for the nonstationary Stokes problem
• Carleman estimates for coefficient inverse problems and numerical applications.
• About stability and regularization of ill-posed elliptic Cauchy problems: the case of Lipschitz domains
• On Carleman estimates for elliptic and parabolic operators. Applications to unique continuation and control of parabolic equations
• About stability and regularization of ill-posed elliptic Cauchy problems: the case ofC^1,1domains
• The stability for the Cauchy problem for elliptic equations
• Carleman estimates for parabolic equations and applications
• Elliptic Partial Differential Equations of Second Order
• Remarques sur l'observabilité pour l'équation de Laplace
• The “Exterior Approach" Applied to the Inverse Obstacle Problem for the Heat Equation
• Tikhonov Regularization by a Reproducing Kernel Hilbert Space for the Cauchy Problem for an Elliptic Equation
• Estimates of initial conditions of parabolic equations and inequalities via lateral Cauchy data
• Global Carleman Inequalities for Parabolic Systems and Applications to Controllability
• Quantitative estimates of unique continuation for parabolic equations, determination of unknown time-varying boundaries and optimal stability estimates
• Inverse problems for partial differential equations
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Quantification of the unique continuation property for the heat equation