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 Ω with a feedback device controlling the external temperature located on the boundary Γ . 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.
Identification of a convolution kernel in a control problem for the heat equation with a boundary memory term / C. Cavaterra, D. Guidetti. - In: ANNALI DI MATEMATICA PURA ED APPLICATA. - ISSN 0373-3114. - 193:3(2014 Jun), pp. 779-816.
Identification of a convolution kernel in a control problem for the heat equation with a boundary memory term
C. Cavaterra
;
2014
Abstract
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 Ω with a feedback device controlling the external temperature located on the boundary Γ . 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.File | Dimensione | Formato | |
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