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We use the spectral method for Gellerstedt problem for Lavrent’ev-Bitsadze equation in a half-strip with Frankl condition on the type change line of the equation. Also a problem from the theory of parabolic-hyperbolic equations with the spectral parameter in the boundary condition is considered. We regard the case of appearing of a multiple eigenvalue by the eigenfunction and the associated function from the root subspace and removing of one eigenfunction with simple eigenvalue. [ABSTRACT FROM AUTHOR]

We consider a classical inhomogeneous boundary problem - the Tricomi problem for parabolic-hyperbolic equation with non-characteristic line of type change. Using spectral method we obtain a solution of a special mixed inhomogeneous problem for the heat transfer equation and afterwards the solution of the Tricomi problem. [ABSTRACT FROM AUTHOR]