Geodesic
Second boundary-value problem for the Lavrent'ev–Bitsadze equation in a rectangular domain with two degeneration lines
Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 137 (2017), pp. 3-16 Cet article a éte moissonné depuis la source Math-Net.Ru

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For a mixed-type equation, we examine the second boundary-value problem and by using the spectral method prove the uniqueness and existence of solutions. The uniqueness criterion is proved based on the completeness property of the biorthogonal system of functions corresponding to the one-dimensional spectral problem. A solution of the problem is constructed as the sum of a biorthogonal series.
Keywords: equation of mixed type, biorthogonal system of functions, completeness, existence and uniqueness of solution. 
@article{INTO_2017_137_a0,
     author = {A. A. Gimaltdinova},
     title = {Second boundary-value problem for the {Lavrent'ev{\textendash}Bitsadze} equation in a rectangular domain with two degeneration lines},
     journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory},
     pages = {3--16},
     year = {2017},
     volume = {137},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/INTO_2017_137_a0/}
}
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A. A. Gimaltdinova. Second boundary-value problem for the Lavrent'ev–Bitsadze equation in a rectangular domain with two degeneration lines. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Differential equations. Mathematical physics, Tome 137 (2017), pp. 3-16. http://geodesic.mathdoc.fr/item/INTO_2017_137_a0/