Cauchy problem for the system of the general hyperbolic differential equations of the forth order with nonmultiple characteristics

Abstract

We consider the Cauchy problem for the hyperbolic differential equation of the forth order with nonmultiple characteristics. We generalize this problem from the similar Cauchy problem for the hyperbolic differential equation of the third order with nonmultiple characteristics which solution was constructed as an analogue of D'Alembert formula. We obtain the regular solution of the Cauchy problem for the hyperbolic differential equation of the forth order with nonmultiple characteristics in an explicit form. This solution is also an analogue of D'Alembert formula. The existence and uniqueness theorem for the regular solution of the Cauchy problem for the hyperbolic differential equation of the forth order with nonmultiple characteristics is formulated as the result of the research. In the paper we consider the Cauchy problem for the system of the general hyperbolic differential equations of the forth order with nonmultiple characteristics.

Keywords

• hyperbolic differential equation of the forth order
• nonmultiple characteristics
• cauchy problem
• d'alembert formula
• system of general hyperbolic differential equations of the forth order