Boundary value problems for a nonstrictly hyperbolic equation of the third order

• Published in: Differential equations Vol. 52; no. 2; pp. 210 - 219
• Main Authors: Korzyuk, V. I., Mandrik, A. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-02-2016; Springer Nature B.V
• Subjects: Boundaries; Boundary conditions; Boundary value problems; Cauchy problems; Difference and Functional Equations; Differential equations; Dirichlet problem; Independent variables; Mathematical analysis; Mathematics; Mathematics and Statistics; Method of characteristics; Ordinary Differential Equations; Partial Differential Equations; Planes; Studies; Uniqueness; Variables; Cauchy Problem; Dirichlet Condition; Mixed Problem; Classical Solution; Hyperbolic Equation
• ISSN: 0012-2661; 1608-3083
• DOI: 10.1134/S0012266116020075

We study classical solutions of boundary value problems for a nonstrictly hyperbolic third-order equation. The equation is posed in a half-strip and a quadrant of the plane of two independent variables. The Cauchy conditions are posed on the lower boundary of the domain, and the Dirichlet conditions are posed on the lateral boundaries. By using the method of characteristics, we find the analytic form of the solution of considered problems. The uniqueness of the solutions is proved.