Bounded and Exponentially Decreasing in time Solutions to High-Order Hyperbolic Equations.
Abstract:
The paper is a continuation of [7] and devoted to high-order hyperbolic operators whose symbols have no zeros in a strip δ-< lmτ <δ+, where τ is the variable duel to the time variable t. Two types of results are presented. In the case δ+ = +∞ (or δ- = -∞) for the corresponding operator we prove the unique solvability of the Cauchy problem on the semiaxis ±t ≥ 0 in the spaces of functions decreasing exponentially as t → ±∞. In the case of finite δ± the unique solvability on the whole time axis in the spaces of bounded in t functions is proved. The results of this paper are based on the estimates are obtained in [7].
Publication language:russian
Research direction:
Mathematical problems and theory of numerical methods
