Well-posedness, smooth dependence and centre manifold reduction for a semilinear hyperbolic system from laser dynamics
✍ Scribed by Mark Lichtner; Mindaugas Radziunas; Lutz Recke
- Publisher
- John Wiley and Sons
- Year
- 2007
- Tongue
- English
- Weight
- 357 KB
- Volume
- 30
- Category
- Article
- ISSN
- 0170-4214
- DOI
- 10.1002/mma.816
No coin nor oath required. For personal study only.
✦ Synopsis
Abstract
We prove existence, uniqueness, regularity and smooth dependence of the weak solution on the initial data for a semilinear, first order, dissipative hyperbolic system with discontinuous coefficients. Such hyperbolic systems have successfully been used to model the dynamics of distributed feedback multisection semiconductor lasers. We show that in a function space of continuous functions the weak solutions generate a smooth skew product semiflow. Using slow fast structure and dissipativity we prove the existence of smooth exponentially attracting invariant centre manifolds for the non‐autonomous model. Copyright © 2006 John Wiley & Sons, Ltd.