Abstract
Publisher Summary This chapter highlights boundary value problems for the equations of mixed type. The problem is concerned with the question: which boundary value problems are well posed for the differential equation of mixed type. An effective numerical algorithm is developed based on the reduction of the boundary value problem into an elliptic problem with unusual non pseudolocal boundary conditions for which the Galerkin procedure works well. This problem is solved both analytically by using and modifying results of Kondratien on elliptic equations in conical regions and numerically by using and modifying standard Laplace inverters. The inverted Cauchy data on the parabolic line is used to obtain the solution in the hyperbolic region.
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