A Nonlocal Problem for a Third Order Parabolic-Hyperbolic Equation with a Spectral Parameter

In this article, a non-classical problem with an integral condition for a parabolic-hyperbolic equation of the third order, has been formulated and investigated. By the method of integral equations, the unique solvability of the considered problem has been proved. The problem is equivalently reduced to a problem for a second order parabolic-hyperbolic equation with unknown right-hand side. The formulas of the Cauchy problem for telegraph equation and the solution of the first boundary value problem for an inhomogeneous parabolic equation were used.

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