Geodesic
The Dirichlet problem for mixed type equation with two lines of degeneracy in a rectangular area
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 19 (2015) no. 4, pp. 634-649

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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, spectral method.
Mots-clés : existence of a solution 
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     author = {A. A. Gimaltdinova},
     title = {The {Dirichlet} problem for mixed type equation  with two lines  of degeneracy  in a rectangular area},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {634--649},
     publisher = {mathdoc},
     volume = {19},
     number = {4},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VSGTU_2015_19_4_a3/}
}
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A. A. Gimaltdinova. The Dirichlet problem for mixed type equation  with two lines  of degeneracy  in a rectangular area. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 19 (2015) no. 4, pp. 634-649. http://geodesic.mathdoc.fr/item/VSGTU_2015_19_4_a3/