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 $(u,f)$.

Cecilia, C., Davide, G. (2015). Identification of a source factor in a control problem for the heat equation with a boundary memory term. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 38(18), 4818-4839 [10.1002/mma.3397].

Identification of a source factor in a control problem for the heat equation with a boundary memory term

GUIDETTI, DAVIDE
2015

Abstract

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 $(u,f)$.
2015
Cecilia, C., Davide, G. (2015). Identification of a source factor in a control problem for the heat equation with a boundary memory term. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, 38(18), 4818-4839 [10.1002/mma.3397].
Cecilia, Cavaterra; Davide, Guidetti
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11585/554414
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