Identification of time and space dependent relaxation kernels for materials with memory related to cylindrical domains. I

DOI10.1006/jmaa.1997.5364zbMath0892.45006OpenAlexW2057721813MaRDI QIDQ1378411

Alfredo Lorenzi, Fabrizio Colombo

Publication date: 21 July 1998

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1997.5364

zbMATH Keywords

inverse problemmaterials with memoryrelaxation kernelfirst-order linear abstract integro-differential equationidentification of the kernel

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Classical linear elasticity (74B05) Abstract integral equations, integral equations in abstract spaces (45N05)

Related Items (18)

A GLOBAL IN TIME EXISTENCE AND UNIQUENESS RESULT FOR A SEMILINEAR INTEGRODIFFERENTIAL PARABOLIC INVERSE PROBLEM IN SOBOLEV SPACES ⋮ Inverse problems for a parabolic integrodifferential equation in a convolutional weak form ⋮ Identification of time and space dependent relaxation kernels for materials with memory related to cylindrical domains. II ⋮ Recovering memory kernels in parabolic transmission problems ⋮ An inverse problem for a parabolic integrodifferential model in the theory of combustion ⋮ A mixed type identification problem related to a phase-field model with memory ⋮ Recovering degenerate kernels in hyperbolic integro-differential equations ⋮ A unified approach to nonlinear integro-differential inverse problems of parabolic type ⋮ A general inverse problem for a memory kernel in one-dimensional viscoelasticity ⋮ A parabolic integro-differential identification problem in a barrelled smooth domain ⋮ Direct and inverse problems for a phase-field model with memory ⋮ Identification of weakly singular relaxation kernels in three-dimensional viscoelasticity ⋮ Global in time results for a class of inverse problems ⋮ Degenerate memory kernels identification problem with flux-type additional conditions ⋮ Local solvability of an inverse problem to the Navier–Stokes equation with memory term ⋮ Quasilinear systems with memory kernels ⋮ A local in time existence and uniqueness result of an inverse problem for the Kelvin-Voigt fluids ⋮ Recovering memory kernels in parabolic transmission problems in infinite time intervals: the non-accessible case

Cites Work

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• Sobolev, Besov and Nikolskii fractional spaces: Imbeddings and comparisons for vector valued spaces on an interval
• Linear parabolic evolution equations in \(L^ p\)-spaces
• Geometric theory of semilinear parabolic equations
• Direct and inverse problems in the theory of materials with memory
• Global existence results for first-order integrodifferential identification problems
• An inverse problem in the theory of materials with memory
• An identification problem for a linear integrodifferential equation occurring in heat flow
• On identification of memory kernels in linear theory of heat conduction
• Inverse problems of memory reconstruction

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