Work

Wave Equation with Slowly Decaying Potential: asymptotics of Solution and Wave Operators

Year: 2010

Type: article

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.

Source: Mathematical Modelling of Natural Phenomena

DOI: 10.1051/mmnp/20105405

Author: S. A. Denisov

Institution: University of Wisconsin–Madison

Language: English

Topic: Spectral Theory in Mathematical Physics

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: bronze

Funder: National Science Foundation

Award: Research in Approximation and Scattering Theory