Cauchy problem for a nonstrictly hyperbolic equation on a half-plane with constant coefficients

Abstract

We consider the Cauchy problem for a nonstrictly hyperbolic equation of arbitrary order with constant coefficients. The operator in the equation is a composition of first-order differential operators. The equation is supplemented with Initial conditions. We find the solution of this problem on a half-plane in analytic form in the case of two independent variables under some conditions on the coefficients.

The classical solution of the mixed problem for the one-dimensional wave equation with the nonsmooth second initial condition

“…. ψ = ψ  Как известно, общее решение неоднородного уравнения представляет собой сумму общего решения однородного уравнения и частного решения неоднородного [6,11]. Пусть :…”

Cauchy problem for some fourth-order nonstrictly hyperbolic equations

“…The general solution for both strictly and nonstrictly hyperbolic equations of arbitrary order was constructed there as well. The case of a nonstrictly hyperbolic equation with the coincidence of all characteristics was considered in [5], and the solutions of the Cauchy problem in all cases of a nonstrictly hyperbolic third-order equation of such a form were obtained in [6].…”