Identification of a convolution kernel in a control problem for the heat equation with a boundary memory term

We consider the evolution of the temperature \(u\) in a material with thermal memory characterized by a time-dependent convolution kernel \(h\). The material occupies a bounded region \(\Omega\) with a feedback device controlling the external temperature located on the boundary \(\Gamma\). Assuming...

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Bibliographic Details
Published in:arXiv.org 2013-10
Main Authors: Cavaterra, Cecilia, Guidetti, Davide
Format: Article
Language:English
Subjects:
Boundary conditions
Convolution
Inverse problems
Kernels
Thermodynamics
Time dependence
Online Access:Get full text
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Summary:We consider the evolution of the temperature \(u\) in a material with thermal memory characterized by a time-dependent convolution kernel \(h\). The material occupies a bounded region \(\Omega\) with a feedback device controlling the external temperature located on the boundary \(\Gamma\). Assuming both \(u\) and \(h\) unknown, we formulate an inverse control problem for an integrodifferential equation with a nonlinear and nonlocal boundary condition. Existence and uniqueness results of a solution to the inverse problem are proved.
ISSN:2331-8422
DOI:10.48550/arxiv.1310.5053