Geodesic
Nonlocal problem with time-dependent Steklov's boundary conditions
Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 4 (2010), pp. 56-64 Cet article a éte moissonné depuis la source Math-Net.Ru

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In this article, the solvability of boundary-value problem for hyperbolic equation with nonlocal conditions $$a_1(t)u_x(0,t)+a_2(t)u_x(1,t)+a_3(t)u(0,t)+a_4(t)u(1,t)=0,$$ $$b_1(t)u_x(0,t)+b_2(t)u_x(1,t)+b_3(t)u(0,t)+b_4(t)u(1,t)=0 $$ is proved. The proof is mainly based on a priori estimates and Galerkin procedure.
Keywords: hyperbolic equation, generalized solution.
Mots-clés : nonlocal conditions 
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     title = {Nonlocal problem with time-dependent {Steklov's} boundary conditions},
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}
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L. S. Pulkina; A. V. Dyuzheva. Nonlocal problem with time-dependent Steklov's boundary conditions. Vestnik Samarskogo universiteta. Estestvennonaučnaâ seriâ, no. 4 (2010), pp. 56-64. http://geodesic.mathdoc.fr/item/VSGU_2010_4_a6/

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