The Solvability of a New Boundary Value Problem with Derivatives on the Boundary Conditions for Forward-Backward Linear Systems Mixed of Keldysh Type in Multivariate Dimension
Issue:
Volume 1, Issue 1, June 2015
Pages:
1-9
Received:
5 June 2015
Accepted:
16 June 2015
Published:
17 June 2015
DOI:
10.11648/j.ijtam.20150101.11
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Abstract: The solvability of the boundary value problem for linear systems of the mixed hyperbolic-elliptic equations of Keldysh type in the multivariate domain with the changing time direction are studied. Applying methods of functional analysis, “ -regularizing”, continuation by the parameter and by means of prior estimates, the existence and uniqueness of generalized and regular solutions of a boundary value problem are established in a weighted Sobolev space.
Abstract: The solvability of the boundary value problem for linear systems of the mixed hyperbolic-elliptic equations of Keldysh type in the multivariate domain with the changing time direction are studied. Applying methods of functional analysis, “ -regularizing”, continuation by the parameter and by means of prior estimates, the existence and uniqueness of...
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The Solvability of a New Boundary Value Problem with Derivatives on the Boundary Conditions for Forward-Backward Semi Linear Systems Mixed of Keldysh Type in Multivariate Dimension
Issue:
Volume 1, Issue 1, June 2015
Pages:
10-20
Received:
21 June 2015
Accepted:
30 June 2015
Published:
1 July 2015
DOI:
10.11648/j.ijtam.20150101.12
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Abstract: Abstract. In present paper we investigate solvability of a new boundary value problem with derivatives on the boundary conditions for semi-linear systems of mixed hyperbolic-elliptic of Keldysh type equations in multivariate dimension with the changing time direction . Considered problem and system equations are new and belong to modern level of partial differential equations, moreover contain partition degenerating elliptic, degenerating hyperbolic, mixed and composite type differential equations. Applying methods of functional analysis, topological methods, “ -regularizing» and continuation by the parameter at the same time with aid of a prior estimates, under assumptions conditions on coefficients of equations of system, the existence and uniqueness of generalized and regular solutions of a boundary value problem are established in a weighted Sobolev’s space. In this work one of main idea, the identity of strong and weak solution is established.
Abstract: Abstract. In present paper we investigate solvability of a new boundary value problem with derivatives on the boundary conditions for semi-linear systems of mixed hyperbolic-elliptic of Keldysh type equations in multivariate dimension with the changing time direction . Considered problem and system equations are new and belong to modern level of pa...
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