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

摘要

We consider the evolution of the temperature $u$ in a material with thermalmemory characterized by a time-dependent convolution kernel $h$. The materialoccupies a bounded region $\Omega$ with a feedback device controlling theexternal temperature located on the boundary $\Gamma$. Assuming both $u$ and$h$ unknown, we formulate an inverse control problem for an integrodifferentialequation with a nonlinear and nonlocal boundary condition. Existence anduniqueness results of a solution to the inverse problem are proved.