This article is cited in 1 scientific paper (total in 1 paper)
Recovery of the coefficient of $u_t$ in the heat equation from a condition of nonlocal observation in time
A. B. Kostin
National Research Nuclear University УMEPhIФ, Kashirskoe sh. 31, Moscow, 115409, Russia
The inverse problem of finding the coefficient $\rho(x)=\rho_0+r(x)$ multiplying $u_t$ in the heat equation is studied. The unknown function $r(x)\geqslant0$ is sought in the class of bounded functions, and $\rho_0$ is a given positive constant. In addition to the initial and boundary conditions (data of the direct problem), a nonlocal observation condition is specified in the form $\int\limits_0^T u(x,t)d\mu(t)=\chi(x)$ with a given measure $d\mu(t)$ and a function $\chi(x)$. The case of integral observation (i.e., $d\mu(t)=\omega(t)dt$) is considered separately. Sufficient conditions for the existence and uniqueness of a solution to the inverse problem are obtained in the form of easy-to-check inequalities. Examples of inverse problems are given for which the assumptions of the theorems proved in this work are satisfied.
coefficient inverse problems, inverse problem for the heat equation, nonlocal observation (or overdetermination) condition, sufficient conditions for the existence and uniqueness of a solution.
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Computational Mathematics and Mathematical Physics, 2015, 55:1, 85–100
A. B. Kostin, “Recovery of the coefficient of $u_t$ in the heat equation from a condition of nonlocal observation in time”, Zh. Vychisl. Mat. Mat. Fiz., 55:1 (2015), 89–104; Comput. Math. Math. Phys., 55:1 (2015), 85–100
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\paper Recovery of the coefficient of $u_t$ in the heat equation from a condition of~nonlocal observation in time
\jour Zh. Vychisl. Mat. Mat. Fiz.
\jour Comput. Math. Math. Phys.
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