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This article is cited in 4 scientific papers (total in 4 papers)
Inverse problem for the diffusion equation in the case of spherical symmetry
A. M. Denisov, S. I. Solov'eva Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992, Russia
Abstract:
The initial boundary value problem for the diffusion equation is considered in the case of spherical symmetry and an unknown initial condition. Additional information used for determining the unknown initial condition is an external volume potential whose density is the Laplace operator applied to the solution of the initial boundary value problem. The uniqueness of the solution of the inverse problem is studied depending on the parameters entering into the boundary conditions. It is shown that the solution of the inverse problem is either unique or not unique up to a one-dimensional linear subspace.
Key words:
diffusion equation, spherical symmetry, unknown initial condition, inverse problem, Sturm-Liouville problem, existence and uniqueness of solution.
Received: 22.05.2013
Citation:
A. M. Denisov, S. I. Solov'eva, “Inverse problem for the diffusion equation in the case of spherical symmetry”, Zh. Vychisl. Mat. Mat. Fiz., 53:11 (2013), 1784–1790; Comput. Math. Math. Phys., 52:11 (2013), 1607–1613
Linking options:
https://www.mathnet.ru/eng/zvmmf9941 https://www.mathnet.ru/eng/zvmmf/v53/i11/p1784
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Abstract page: | 394 | Full-text PDF : | 103 | References: | 58 | First page: | 39 |
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