Geodesic
An Approach to the Solution of the Initial Boundary-Value Problem for Systems of Fourth-Order Hyperbolic Equations
Matematičeskie zametki, Tome 108 (2020) no. 1, pp. 3-16

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The initial boundary-value problem for systems of fourth-order partial differential equations with two independent variables is considered. By using a new unknown eigenfunction, the problem under consideration is reduced to an equivalent nonlocal problem for a system of second-order hyperbolic-type integro-differential equations with integral conditions. An algorithm for finding an approximate solution of the resulting equivalent problem is proposed, and its convergence is proved. Conditions for the existence of a unique classical solution of the initial boundary-value problem for systems of fourth-order differential equations are established in terms of the coefficients of the system and the boundary matrices.
Keywords: system of fourth-order hyperbolic equations, initial boundary-value problem, hyperbolic-type integro-differential equation, nonlocal problem, solvability. 
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     author = {A. T. Assanova and Zh. S. Tokmurzin},
     title = {An {Approach} to the {Solution} of the {Initial} {Boundary-Value} {Problem} for {Systems} of {Fourth-Order} {Hyperbolic} {Equations}},
     journal = {Matemati\v{c}eskie zametki},
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A. T. Assanova; Zh. S. Tokmurzin. An Approach to the Solution of the Initial Boundary-Value Problem for Systems of Fourth-Order Hyperbolic Equations. Matematičeskie zametki, Tome 108 (2020) no. 1, pp. 3-16. http://geodesic.mathdoc.fr/item/MZM_2020_108_1_a0/