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On Identification of Memory Kernels in Linear Viscoelasticity
Author(s) -
Wolfersdorf L. V.
Publication year - 1993
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19931610115
Subject(s) - mathematics , viscoelasticity , kernel (algebra) , identification (biology) , inverse problem , boundary value problem , constitutive equation , mathematical analysis , parameter identification problem , optimal control , displacement (psychology) , mathematical optimization , pure mathematics , psychology , model parameter , botany , physics , finite element method , biology , psychotherapist , thermodynamics
The inverse problem of identification of the memory kernel in the linear constitutive stress‐strain‐relation of Boltzmann type is reduced to an optimal control problem for an initial‐boundary‐value problem of the related wave equation for the displacement. For the control problem the existence of an optimal control is proved, where both classical and generalized solutions of the equation are dealt with. Further the existence and an expression for the gradient of the cost functional are derived.