Geodesic
Well-posedness of the Dirichlet and Poincar\'e problems for~one class of hyperbolic equations in~a~ multidimensional~domain
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 21 (2017) no. 2, pp. 209-220

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In early works the author studied the Dirichlet and Poincaré problems for multidimensional hyperbolic equations, which shows the well-posedness of these problems in cylindrical domains, significantly dependent on the height of the considered cylindrical domain. Here a multidimensional region inside a characteristic cone is considered, in which the Dirichlet and Poincaré problems have unique solutions for one class of hyperbolic equations.
Keywords: multidimensional hyperbolic equation, Dirichlet and Poincaré problems, well-posedness, functional-integral equation.
Mots-clés : multidimensional domain 
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     title = {Well-posedness of the {Dirichlet} and {Poincar\'e} problems for~one class of hyperbolic equations in~a~ multidimensional~domain},
     journal = {Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences},
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S. A. Aldashev. Well-posedness of the Dirichlet and Poincar\'e problems for~one class of hyperbolic equations in~a~ multidimensional~domain. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, Tome 21 (2017) no. 2, pp. 209-220. http://geodesic.mathdoc.fr/item/VSGTU_2017_21_2_a0/