Solution of the cauchy problem for a hyperbolic equation with constant coefficients in the case of two independent variables

• Published in: Differential equations Vol. 48; no. 5; pp. 707 - 716
• Main Authors: Korzyuk, V. I., Kozlovskaya, I. S.
• Format: Journal Article
• Language: English
• Published: Dordrecht SP MAIK Nauka/Interperiodica 01-05-2012; Springer Nature B.V
• Subjects: Cauchy problem; Cauchy problems; Difference and Functional Equations; Differential equations; Independent variables; Mathematical analysis; Mathematics; Mathematics and Statistics; Operators; Ordinary Differential Equations; Partial Differential Equations; Planes; Studies; Cauchy Problem; General Solution; Volterra Operator; Hyperbolic Equation; Computer Algebra System
• ISSN: 0012-2661; 1608-3083
• DOI: 10.1134/S0012266112050096

On the plane, we consider a linear partial differential equation of arbitrary order of hyperbolic type. The operator in the equation is a composition of first-order differential operators. The equation is accompanied with Cauchy conditions. For the equation, we obtain an analytic form of the general solution, from which we single out the unique classical solution of the Cauchy problem.