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Wave Equation with Slowly Decaying Potential: asymptotics of Solution 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-summable potential. We establish the long-time asymptotics of solutions by, first, studying the stationary problem and, second, using the spectral representation for the evolution equation. In particular, we prove that part of the wave travels ballistically if q ∈ L2(ℝ+) and this result is sharp.

Keywords

wave equationsquare-summable potentialwave operators
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 5 , Issue 4: Spectral problems. Issue dedicated to the memory of M. Birman , 2010 , pp. 122 - 149
Copyright
© EDP Sciences, 2010

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