## Two problems with shifts for an equation of the mixed-composite type.(Russian)Zbl 0541.35057

A. M. Nakhushev has studied boundary value problems for hyperbolic equations and equations of mixed type with boundary conditions on the characteristics [Differ. Uravn. 5, 44-59 (1969; Zbl 0172.143)]. Continuing those investigations the author considers in a domain typical for the Tricomi problem two boundary value problems for the equation $$w_{xxx}+sgn y\quad w_{yyx}=0$$. The shift conditions are linear combinations connecting values of the unknown function on the symmetry line of the hyperbolic part of the domain and on characteristics passing through one of the ends of the symmetry line. The existence of a unique solution of the problems is proved.
Reviewer: K.Barckow

### MSC:

 35M99 Partial differential equations of mixed type and mixed-type systems of partial differential equations 35A05 General existence and uniqueness theorems (PDE) (MSC2000)

Zbl 0172.143
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