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WAVE EQUATION WITH SLOWLY DECAYING POTENTIAL: ASYMPTOTICS OF SOLUTION AND WAVE OPERATORS

By Sergey A. Denisov

Abstract

Abstract. In this paper, we consider one-dimensional wave equation with real-valued square-summable potential. We establish the long-time asymptotics of solutions by, first, studying the stationary problem and, secondly, using the spectral representation for the evolution equation. In particular, we prove that part of the wave travels ballistically if q ∈ L 2 (R +) and this result is sharp

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