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arXiv · 1310.5053

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

Cecilia Cavaterra·Davide Guidetti
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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 $\Omega$ 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.

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Cecilia Cavaterra, Davide Guidetti. 2013-10-18. Identification of a convolution kernel in a control problem for the heat equation with a boundary memory term. https://doi.org/10.1007/s10231-012-0301-y

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