Exponential Dichotomy of Solutions to High-Order Hyperbolic Equations

L. R. Volevich, A. R. Shirikyan


Abstract: The paper is a continuation of previous works and is devoted to investigation of linear high-order hyperbolic equations with variable coefficients. The basic assumption is that the symbol of the operator in the left-hand side of the equation has no zeros in a strip |Im$\tau$|< $\delta$, $\delta$ > 0, where $\tau$ is the variable dual to the time variable t. We prove the exponential dichotomy property for solutions to the homogeneous equation. Furthermore, we give an explicit description of the spaces of Cauchy's data for exponentially decreasing as t \to ±\infty solutions to the homogeneous equation.