The formula of the solution for some classes of initial boundary value problems for the hyperbolic equation with two independent variables

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Abstract

A new representation is proved of the solutions of initial boundary value problems for the equation of the form uxx(x, t) + r(x)ux(x, t) − q(x)u(x, t) = utt(x, t) + μ(x)ut(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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