Energy Estimates for a Class of High-Order Hyperbolic Equations.
Abstract:
The present paper is the first part of an investigation of some problems related to the solvability of high-order hyperbolic equations in spaces of functions bounded or almost-periodic with respect to time variable t. High-order operators are treated under the additional condition on lower terms: the full symbol of the operator has no zeros in a strip δ-< lmτ <δ+, where τ and t are dual variables, and δ± can assign the value ±∞. In this context Leray's separating operator method is developed and two-sided energy estimates in the case of constant coefficients are obtained. These estimates are extended to the operators with variable coefficients if the derivatives of the coefficients are sufficiently 'small''.
Publication language:russian
Research direction:
Mathematical problems and theory of numerical methods
