Geodesic
One Goursat problem in a~Sobolev space
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2011), pp. 54-64

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In this paper we consider a hyperbolic-type differential equation with $L_p$-coefficients in a three-dimensional space. For this equation we study the Goursat problem with nonclassical boundary constraints not requiring matched conditions. We prove the equivalence of these boundary conditions to classical ones in the case when one seeks for a solution to the stated problem in an anisotropic space introduced by S. L. Sobolev. In addition, we prove the correct solvability of the Goursat problem by the method of integral equations.
Keywords: hyperbolic equation, three-dimensional Goursat problem, equations with $L_p$-coefficients. 
@article{IVM_2011_2_a5,
     author = {I. G. Mamedov},
     title = {One {Goursat} problem in {a~Sobolev} space},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {54--64},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2011_2_a5/}
}
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I. G. Mamedov. One Goursat problem in a~Sobolev space. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2011), pp. 54-64. http://geodesic.mathdoc.fr/item/IVM_2011_2_a5/