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The existence and uniqueness of a new boundary value problem (type of problem “E”) for linear system equations of the mixed hyperbolic-elliptic type in the multivariate dimension with the changing time direction. (English) Zbl 1347.35180

Summary: The existence and uniqueness of the boundary value problem for linear systems equations of the mixed hyperbolic-elliptic type in the multivariate domain with the changing time direction are studied. Applying methods of functional analysis, “\(\varepsilon\)-regularizing” continuation by the parameter and by means of prior estimates, the existence and uniqueness of generalized and regular solutions of a boundary problem are established in a weighted Sobolev space.

MSC:

35M11 Initial value problems for PDEs of mixed type
35A01 Existence problems for PDEs: global existence, local existence, non-existence
35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness
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