Geodesic
The boundary-value problem for the Lavrent'ev--Bitsadze equation with unknown right-hand side
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2011), pp. 44-52

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We study the inverse problem for the Lavrent'ev–Bitsadze equation in a rectangular domain. We construct its solution as a series in eigenfunctions for the corresponding problem on eigenvalues and establish a criterion for its uniqueness. We also prove the stability of the obtained solution.
Keywords: mixed-type equation, inverse problem, spectral method, uniqueness, stability.
Mots-clés : existence 
@article{IVM_2011_5_a5,
     author = {K. B. Sabitov and I. A. Khadzhi},
     title = {The boundary-value problem for the {Lavrent'ev--Bitsadze} equation with unknown right-hand side},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {44--52},
     publisher = {mathdoc},
     number = {5},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_5_a5/}
}
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K. B. Sabitov; I. A. Khadzhi. The boundary-value problem for the Lavrent'ev--Bitsadze equation with unknown right-hand side. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2011), pp. 44-52. http://geodesic.mathdoc.fr/item/IVM_2011_5_a5/