Differential Equations and Mathematical Physics

Well-posedness of the Dirichlet and Poincaré problems for one class of hyperbolic equations in a multidimensional domain

S. A. Aldashev

Kazakh National Pedagogical University, Almaty, 480100, Kazakhstan

Abstract: 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, multidimensional domain, well-posedness, functional-integral equation.

UDC: 517.955.2

MSC: 35L10, 35R25

Received: May 31, 2016
Revised: April 11, 2017
Accepted: June 12, 2017
First online: July 7, 2017

DOI: 10.14498/vsgtu1494

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