Stability properties of an inverse parabolic problem with unknown boundaries

DOI10.1007/s10231-005-0152-xzbMath1232.35192OpenAlexW1979203875MaRDI QIDQ661073

Luca Rondi, Michele Di Cristo, Sergio Vessella

Publication date: 18 February 2012

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/2434/612294

zbMATH Keywords

stabilityinverse problemsunique continuationBessel functionsparabolic equations

Mathematics Subject Classification ID

Inverse problems for PDEs (35R30) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Applications of hypergeometric functions (33C90) Continuation and prolongation of solutions to PDEs (35B60) Parabolic equations and parabolic systems (35K99)

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Cites Work

• Spherical harmonics
• Quantitative estimates of unique continuation for parabolic equations and inverse initial-boundary value problems with unknown boundaries
• Exponential instability in an inverse problem for the Schrödinger equation
• On the numerical solution of an inverse boundary value problem for the heat equation
• Stability and reconstruction for an inverse problem for the heat equation
• Some inverse problems for the diffusion equation
• Examples of exponential instability for inverse inclusion and scattering problems
• A stability result in the localization of cavities in a thermic conducting medium
• Carleman Estimates, Optimal Three Cylinder Inequality, and Unique Continuation Properties for Solutions to Parabolic Equations
• Stable determination of cavities in elastic bodies
• On an inverse problem arising in continuous casting of steel billets
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