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| We consider a material with thermal memory occupying a bounded region $\Omega$ with boundary $\Gamma$.
The evolution of the temperature $u(t,x)$ is described by an integrodifferential parabolic equation containing a heat source of the form $f(t)z_0(x)$.
We formulate an initial and boundary value control problem based on a feedback device located on $\Gamma$ and prescribed by means of a quite general memory operator.
Assuming both $u$ and the source factor $f$ unknown, we study the corresponding inverse and control problem on account of an additional information.
We prove a result of existence and uniqueness of the solution $(u,f)$. |
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