Geodesic
Initial-boundary problem for parabolic-hyperbolic equation with loaded summands
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2015), pp. 31-42

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In the paper we find necessary and sufficient conditions for uniqueness of a solution to initial-boundary problem for a loaded equation of mixed parabolic-hyperbolic type. The solution is constructed in the form of sums of a series in eigenfunctions of the corresponding one-dimensional problem on eigenvalues. At a substantiation of convergence of series arises the problem of small denominators. Under certain conditions on these data we obtain an estimation of separation from scratch small denominator that has allowed to prove the existence theorem in the class of regular solutions.
Keywords: equation of mixed type with loaded summands, initial-boundary problem, uniqueness, stability.
Mots-clés : existence 
@article{IVM_2015_6_a4,
     author = {K. B. Sabitov},
     title = {Initial-boundary problem for parabolic-hyperbolic equation with loaded summands},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {31--42},
     publisher = {mathdoc},
     number = {6},
     year = {2015},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2015_6_a4/}
}
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K. B. Sabitov. Initial-boundary problem for parabolic-hyperbolic equation with loaded summands. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2015), pp. 31-42. http://geodesic.mathdoc.fr/item/IVM_2015_6_a4/