Over-determined boundary value problems for elliptic partial differential equations and their applications to waves diffraction theory.

I. E. Pleshchinskaya   ; N. B. Pleschinskii

Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Kazanskii Gosudarstvennyi Universitet. Uchenye Zapiski. Seriya Fiziko-Matematichaskie Nauki, Tome 147 (2005) no. 3, pp. 4-32

Résumé

The review of the results of investigation of the boundary value problems with redundant boundary conditions for the partial differential equations is given. The necessary and sufficient conditions of solvability for the over-determined problems are obtained by the integral Fourier transform method in the classes of distributions for the equations with constant coefficients. The Helmholtz equation, the Maxwell equations and sets of equations for the dynamic elasticity theory are considered as examples. These solvability conditions are used for reducing some problems of propagation and diffraction of electromagnetic and elastic waves theory to the integral and summatorial equations.

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