Geodesic
Inverse problem for degenerate parabolic-hyperbolic equation with nonlocal boundary condition
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2015), pp. 46-59

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For a mixed type equation with a power-law degeneration we consider the inverse problem on finding an unknown right side. We establish a uniqueness criterion of solution to the problem with a nonlocal condition that connects the normal derivative of the sought-for solution, which belongs to different types of studied equations. The solution is constructed in the form of sums of a series in eigenfunctions of the corresponding one-dimensional spectral problem. We also prove stability of the solution to the non-local boundary condition.
Keywords: equation of mixed type, spectral method, uniqueness, stability.
Mots-clés : existence 
@article{IVM_2015_1_a3,
     author = {K. B. Sabitov and S. N. Sidorov},
     title = {Inverse problem for degenerate parabolic-hyperbolic equation with nonlocal boundary condition},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {46--59},
     publisher = {mathdoc},
     number = {1},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_1_a3/}
}
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K. B. Sabitov; S. N. Sidorov. Inverse problem for degenerate parabolic-hyperbolic equation with nonlocal boundary condition. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2015), pp. 46-59. http://geodesic.mathdoc.fr/item/IVM_2015_1_a3/