Classical solution of the first mixed problem for a third-order hyperbolic equation with the wave operator

• Published in: Differential equations Vol. 50; no. 4; pp. 489 - 501
• Main Authors: Korzyuk, V. I., Mandrik, A. A.
• Format: Journal Article
• Language: English
• Published: Moscow Pleiades Publishing 01-04-2014; Springer Nature B.V
• Subjects: Boundaries; Boundary value problems; Cauchy problems; Difference and Functional Equations; Differential equations; Dirichlet problem; Exact solutions; Independent variables; Mathematical analysis; Mathematics; Mathematics and Statistics; Operators; Ordinary Differential Equations; Partial Differential Equations; Studies; Uniqueness; Cauchy Problem; Matching Condition; Classical Solution; Lower Base; Hyperbolic Equation
• ISSN: 0012-2661; 1608-3083
• DOI: 10.1134/S0012266114040077

We study the classical solution of the boundary value problem for a third-order hyperbolic equation defined on the plane in a half-strip with the Cauchy conditions on the lower base of the domain and with the Dirichlet conditions on the lateral boundary. By the method of characteristics, in the case of two independent variables, we find the solution of the problem in closed form and prove its uniqueness.