Geodesic
A three-dimensional analog of the Tricomi problem for a~parabolic-hyperbolic equation
Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 2, pp. 34-44

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For a parabolic-hyperbolic equation, we study the three-dimensional analog of the Tricomi problem with a noncharacteritic plane on which the type of the equation changes. The uniqueness of the solution to the problem is proved by the method of a priori estimates, and the existence of a solution is reduced to the existence of a solution to a Volterra integral equation of the second kind.
Keywords: parabolic-hyperbolic equation, Tricomi problem, maximum principle, uniqueness, integral equation.
Mots-clés : Fourier transform, existence 
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     author = {Yu. P. Apakov},
     title = {A three-dimensional analog of the {Tricomi} problem for a~parabolic-hyperbolic equation},
     journal = {Sibirskij \v{z}urnal industrialʹnoj matematiki},
     pages = {34--44},
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     url = {http://geodesic.mathdoc.fr/item/SJIM_2011_14_2_a4/}
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Yu. P. Apakov. A three-dimensional analog of the Tricomi problem for a~parabolic-hyperbolic equation. Sibirskij žurnal industrialʹnoj matematiki, Tome 14 (2011) no. 2, pp. 34-44. http://geodesic.mathdoc.fr/item/SJIM_2011_14_2_a4/