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Wave Equation with Slowly Decaying Potential: asymptotics ofSolution and Wave Operators

Published online by Cambridge University Press:  12 May 2010

S. A. Denisov
S. A. Denisov*
Affiliation:
University of Wisconsin–Madison, Mathematics Department 480 Lincoln Dr., Madison, WI, 53706, USA
*
1 E-mail: denissov@math.wisc.edu
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Abstract

In this paper, we consider one-dimensional wave equation with real-valued square-summablepotential. We establish the long-time asymptotics of solutions by, first, studying thestationary problem and, second, using the spectral representation for the evolutionequation. In particular, we prove that part of the wave travels ballistically ifq ∈ L 2(ℝ+) and this result issharp.

Keywords

wave equationsquare-summable potentialwave operators

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