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An identification problem for a linear integrodifferential equation occurring in heat flow
Author(s) -
Grasselli Maurizio
Publication year - 1992
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.1670150304
Subject(s) - overdetermined system , mathematics , heat equation , heat flow , flow (mathematics) , mathematical analysis , convolution (computer science) , linear equation , identification (biology) , set (abstract data type) , geometry , thermodynamics , physics , thermal , machine learning , artificial neural network , computer science , programming language , botany , biology
A linear integrodifferential equation describing the heat flow in a material with memory is considered. This equation contains a pair of time‐dependent convolution kernels that are unknown. Such kernels are recovered by using an overdetermined set of data. A local existence theorem for small times and the continuous dependence of the solutions on the data are shown.