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A linear boundary value problem for a system of composite partial differential equations
A. D. Dzhuraev
A two-variable system of first-order partial differential equations is investigated which has, in the region under consideration, one family of real characteristics and two families of imaginary characteristics. A general linear boundary value problem for the system is studied. It is proved that if a certain condition is imposed on the coefficients in the boundary conditions, there is only a finite number of linearly independent solutions of the homogeneous problem and of the adjoint homogeneous problem. A formula for the index of the above problem is derived and a necessary and sufficient condition for the solvability of the inhomogeneous problem is obtained in terms of the homogeneous adjoint problem.
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Mathematics of the USSR-Izvestiya, 1967, 1:3, 525–543
MSC: 35J25, 35Q15, 45E05
A. D. Dzhuraev, “A linear boundary value problem for a system of composite partial differential equations”, Izv. Akad. Nauk SSSR Ser. Mat., 31:3 (1967), 543–562; Math. USSR-Izv., 1:3 (1967), 525–543
Citation in format AMSBIB
\paper A linear boundary value problem for a system of composite partial differential equations
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\jour Math. USSR-Izv.
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Martin Costabel, “A contribution to the theory of singular integral equations with carleman shift”, Integr equ oper theory, 2:1 (1979), 11
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