Geodesic
A uniqueness criterion for solutions of~the~Dirichlet problem for a loaded equation with~the~Lavrent'ev-Bitsadze operator
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2013), pp. 37-45

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The first boundary value problem was considered for the second order loaded differential equation of mixed elliptic-hyperbolic type in a rectangular region. The local and nonlocal problems for the loaded partial differential equations of the individual and mixed types have been previously studied in areas where the hyperbolic part is the characteristic triangle. In this work, in contrast to the well-known ones, necessary and sufficient conditions of the uniqueness of this problem solution were found by the method of spectral analysis.
Keywords: loaded equation of mixed type, Dirichlet problem, spectral method, criterion of uniqueness. 
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     author = {O. A. Arhipova},
     title = {A uniqueness criterion for solutions {of~the~Dirichlet} problem for a loaded equation {with~the~Lavrent'ev-Bitsadze} operator},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
     pages = {37--45},
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O. A. Arhipova. A uniqueness criterion for solutions of~the~Dirichlet problem for a loaded equation with~the~Lavrent'ev-Bitsadze operator. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 1 (2013), pp. 37-45. http://geodesic.mathdoc.fr/item/VSGTU_2013_1_a4/