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) + ?(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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