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Unique Solvability of Nonlocal Boundary Value Problems for Systems of Hyperbolic Equations

Unique Solvability of Nonlocal Boundary Value Problems for Systems of Hyperbolic Equations Differential Equations, Vol. 39, No. 10, 2003, pp. 1414–1427. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 10, 2003, pp. 1343–1354. Original Russian Text Copyright c 2003 by Asanova, Dzhumabaev. PARTIAL DIFFERENTIAL EQUATIONS Unique Solvability of Nonlocal Boundary Value Problems for Systems of Hyperbolic Equations A. T. Asanova and D. S. Dzhumabaev Institute for Mathematics, Ministry of Education and Science, Almaty, Kazakhstan Received June 10, 2003 On =[0;! ] [0;! ], we consider the boundary value problem 1 2 @ u @u @u = A(x;y) + B(x;y) + C (x;y)u + f (x;y); (1) @x@y @x @y u(0;y)= (y);y 2 [0;! ]; (2) @u(x; 0) @u(x; 0) P (x) + P (x) + P (x)u(x; 0) 2 1 0 @x @y (3) @u (x;! ) @u (x;! ) 2 2 + S (x) + S (x) + S (x)u (x;! )= '(x);x 2 [0;! ]; 2 1 0 2 1 @x @y where the n  n matrices A(x;y), B(x;y), C (x;y), P (x), P (x), P (x), S (x), S (x), and S (x) 2 1 0 2 1 0 and the n-vector functions f (x;y)and '(x) are continuous on and [0;! ], respectively, and the n-vector function (y) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Differential Equations Springer Journals

Unique Solvability of Nonlocal Boundary Value Problems for Systems of Hyperbolic Equations

Asanova, A.; Dzhumabaev, D.
Differential Equations , Volume 39 (10) – Oct 11, 2004
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References (3)

Publisher
Springer Journals
Copyright
Copyright © 2003 by MAIK “Nauka/Interperiodica”
Subject
Mathematics; Difference and Functional Equations; Ordinary Differential Equations; Partial Differential Equations
ISSN
0012-2661
eISSN
1608-3083
DOI
10.1023/B:DIEQ.0000017915.18858.d4
Publisher site
See Article on Publisher Site

Abstract

Differential Equations, Vol. 39, No. 10, 2003, pp. 1414–1427. Translated from Differentsial'nye Uravneniya, Vol. 39, No. 10, 2003, pp. 1343–1354. Original Russian Text Copyright c 2003 by Asanova, Dzhumabaev. PARTIAL DIFFERENTIAL EQUATIONS Unique Solvability of Nonlocal Boundary Value Problems for Systems of Hyperbolic Equations A. T. Asanova and D. S. Dzhumabaev Institute for Mathematics, Ministry of Education and Science, Almaty, Kazakhstan Received June 10, 2003 On =[0;! ] [0;! ], we consider the boundary value problem 1 2 @ u @u @u = A(x;y) + B(x;y) + C (x;y)u + f (x;y); (1) @x@y @x @y u(0;y)= (y);y 2 [0;! ]; (2) @u(x; 0) @u(x; 0) P (x) + P (x) + P (x)u(x; 0) 2 1 0 @x @y (3) @u (x;! ) @u (x;! ) 2 2 + S (x) + S (x) + S (x)u (x;! )= '(x);x 2 [0;! ]; 2 1 0 2 1 @x @y where the n  n matrices A(x;y), B(x;y), C (x;y), P (x), P (x), P (x), S (x), S (x), and S (x) 2 1 0 2 1 0 and the n-vector functions f (x;y)and '(x) are continuous on and [0;! ], respectively, and the n-vector function (y)

Journal

Differential Equations – Springer Journals

Published: Oct 11, 2004

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