This article is cited in 2 papers

Inverse problem for the diffusion equation with overdetermination in the form of an external volume potential

A. M. Denisov

Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, 119992 Russia

Abstract: An initial-boundary value problem for the diffusion equation with an unknown initial condition is considered. Additional information used for determining the unknown initial condition is an external volume potential whose density is the Laplacian calculated for the solution of the initial-boundary value problem. Uniqueness theorems for the inverse problem are proved in the case when the spatial domain of the initial-boundary value problem is a spherical layer or a parallelepiped.

Key words: diffusion equation, unknown initial condition, inverse problem, volume potential, eigenfunctions of Laplacian, uniqueness theorems.

UDC: 519.633.9

Received: 18.03.2011

 English version: Computational Mathematics and Mathematical Physics, 2011, 51:9, 1588–1595

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