Some non-local problems for the parabolic-hyperbolic type equation with complex spectral parameter

In the present paper the unique solvability of two non-local problems for the mixed parabolic-hyperbolic type equation with complex spectral parameter is proved. Sectors for values of the spectral parameter where these problems have unique solutions are shown. Uniqueness of the solution is proved by the method of energy integral and existence is proved by the method of integral equations. In particular cases, eigenvalues and corresponding eigenfunctions of the studied problems are found. (C) 2008 WILEY-VCH Verlag GmbH & Co. KGaA. Weinheim.