The Dirichlet problem for mixed type equation with two lines of degeneracy in a rectangular area

Abstract

We study the first boundary value problem for the elliptic-hyperbolic type equation with two perpendicular lines of change of type and spectral parameter. We prove the existence and uniqueness of the solution. In the proof of the uniqueness of solution we use the completeness of biorthogonal system in space $L_2$ . When building a solution as the sum of a series there is a problem of small denominators. We obtained estimates of the denominators of the separation from zero.

Keywords

• mixed type equation
• dirichlet problem
• uniqueness
• existence of a solution
• spectral method