Inverse problems for determining boundary regimes for some equations of Sobolev type

A. I. Kozhanov

Vestnik Ûžno-Uralʹskogo gosudarstvennogo universiteta. Seriâ, Matematičeskoe modelirovanie i programmirovanie, Tome 9 (2016) no. 2, pp. 37-45

Résumé

We study the solvability of the inverse problems of finding a solution to some Sobolev type equations along with the unknown coefficients of a special type defining the boundary modes (boundary data) in the first or the third initial-boundary value problems respectively. The presence of an unknown coefficient in such problems supposes that there is an additional condition — an overdetermination condition along with the initial and boundary conditions that are typical for the corresponding class of differential equations. In the present work this condition is represented by the integral overdetermination, when some integrals by the cross-section of the cylindrical domain by planes $t=\mathrm{const}$ are equal to zero. The goal of this research is to prove the existence of regular (with all needed generalized according to S. L. Sobolev derivatives) solutions of equation. Along with the specific results there are also some of their possible generalizations.

Détail

Keywords: Sobolev type equations; inverse problems; unknown boundary data; integral overdetermination; regular solutions; solvability.

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