| Issue |
Math. Model. Nat. Phenom.
Volume 5, Number 4, 2010
Spectral problems. Issue dedicated to the memory of M. Birman
|
|
|---|---|---|
| Page(s) | 122 - 149 | |
| DOI | https://doi.org/10.1051/mmnp/20105405 | |
| Published online | 12 May 2010 | |
Wave Equation with Slowly Decaying Potential: asymptotics of Solution and Wave Operators
University of Wisconsin–Madison, Mathematics Department
480 Lincoln Dr., Madison, WI, 53706,
USA
1 E-mail: denissov@math.wisc.edu
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.
Mathematics Subject Classification: 35L05
Key words: wave equation / square-summable potential / wave operators
© EDP Sciences, 2010
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