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Differential Equations, Vol. 41, No. 3, 2005, pp. 352–363. Translated from Differentsial'nye Uravneniya, Vol. 41, No. 3, 2005, pp. 337–346. Original Russian Text Copyright c 2005 by Asanova, Dzhumabaev. PARTIAL DIFFERENTIAL EQUATIONS Well-Posed Solvability of Nonlocal Boundary Value Problems for Systems of Hyperbolic Equations A. T. Asanova and D. S. Dzhumabaev Institute of Mathematics, Ministry of Education and Science, Almaty, Kazakhstan Received September 5, 2003 In the domain =[0;!] [0;T ], we consider the following boundary value problem with data on characteristics for a system of second-order hyperbolic equations with two independent variables: @ u @u @u = A(x;t) + B(x;t) + C (x;t)u + f (x;t); (1) @t@x @x @t u(0;t)= (t);t 2 [0;T ]; (2) @u(x; 0) @u(x; 0) P (x) + P (x) + P (x)u(x; 0) 2 1 0 @x @t (3) @u(x;T ) @u(x;T ) + S (x) + S (x) + S (x)u(x;T)= '(x);x 2 [0;!]; 2 1 0 @x @t where u = colon (u ;u ;:::;u ), the n n matrices A(x;t), B(x;t), C (x;t), P (x), P (x), P (x), 1 2 n 2 1 0 S (x), S (x), and S (x)and the n-vector functions f (x;t)and '(x)
Differential Equations – Springer Journals
Published: May 26, 2005
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