Abstract
A new representation is proved of the solutions of initial boundary value problems for the equation of the form u xx (x, t) + r(x)u x (x, t) − q(x)u(x, t) = u tt (x, t) + μ(x)u t (x, t) in the section (under boundary conditions of the 1st, 2nd, or 3rd type in any combination). This representation has the form of the Riemann integral dependent on the x and t over the given section.
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Original Russian Text © V.L. Pryadiev, A.V. Pryadiev, 2007, published in Avtomatika i Telemekhanika, 2007, No. 2, pp. 138–151.
This work was supported by the Russian Foundation for Basic Research, project no. 04-01-00049 and the grant of President of the Russian Federation, project no. NSH-1643.2003.
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Pryadiev, V.L., Pryadiev, A.V. The formula of the solution for some classes of initial boundary value problems for the hyperbolic equation with two independent variables. Autom Remote Control 68, 337–350 (2007). https://doi.org/10.1134/S0005117907020142
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DOI: https://doi.org/10.1134/S0005117907020142