A necessary and sufficient condition on scattering for the regularly hyperbolic systems

Details A necessary and sufficient condition on scattering for the regularly hyperbolic systems A necessary and sufficient condition on scattering for the regularly hyperbolic systems

2010-08-27

arxiv.org/abs/1008.4644v1

Mathematics

Analysis of PDEs

16 pages

Scientific paper

The present paper is devoted to finding a necessary and sufficient condition on the occurence of scattering for the regularly hyperbolic systems with time-dependent coefficients whose time-derivatives are integrable over the real line. More precisely, it will be shown that the solutions are asymptotically free if the coefficients are stable in the sense of the Riemann integrability as time goes to infinity, while each nontrivial solution is never asymptotically free provided that the coefficients are not R-stable as times goes to infinity. As a by-product, the scattering operator can be constructed. It is expected that the results obtained in the present paper would be brought into the study of the asymptotic behaviour of Kirchhoff systems.

Affiliated with

Also associated with

No associations

Rating

A necessary and sufficient condition on scattering for the regularly hyperbolic systems does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with A necessary and sufficient condition on scattering for the regularly hyperbolic systems, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and A necessary and sufficient condition on scattering for the regularly hyperbolic systems will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-331200