Singular Perturbations in Hysteresis

This book brings together many important recent developments in the analysis of singular perturbation and hysteresis phenomena.

Michael P. Mortell (Edited by), Michael P. Mortell (Author), Robert E. O'Malley (Edited by), Robert E. O`malley (Author), Alexei Pokrovskii (Author), Vladimir Sobolev (Author)

9780898715972

Paperback / softback, published 30 June 2005

358 pages
23.6 x 16.8 x 1.8 cm, 0.538 kg

This book unifies many important recent developments in the analysis of singular perturbation and hysteresis phenomena in an accessible and comprehensive fashion. In April 2002 at University College Cork in Ireland, the editors conducted a workshop to provide a forum for experts to share their interests and knowledge. For this book, the editors have compiled research from those practitioners in areas such as reacting systems, semiconductor lasers, shock phenomena in economic modeling, and fluid mechanics, all with an emphasis on hysteresis and singular perturbations. A basic introduction to hysteresis and singular perturbation theory is included, with simple examples from both physics and mathematics. Later chapters address: applications of hysteresis to economics; various aspects of the asymptotic theory of singularly perturbed systems; typical problems of the asymptotic theory of contrast structures; and the geometrical approach to an investigation of models with singular perturbations and hysteresis.

Preface
1. A naïve view of time relaxation and hysteresis A. Pokrovskii and V. Sobolev
2. Frustration minimization, hysteresis and the El Farol problem R. Cross, M. Grinfeld, H. Lamba and A. Pittock
3. Hysteresis in singularly perturbed problems P. Krejí
4. Combined asymptotic expansions E. Benoît, A. Fruchard and A. El Hamidi
5. Contrast structures of alternating type A. Vasilieva
6. Multi-dimensional internal layers N. Nefedov
7. Geometry of singular perturbations: critical cases V. Sobolev
8. Black swans and canards in laser and combustion models E. Shchepakina, V. Sobolev
9. Multi-scale analysis of pressure driven flames V. Bykov, I. Goldfarb and V. Gol'dshtein
10. Split-hyperbolicity, hysteresis and Lang-Kobayashi equations A. Pokrovskii, O. Rasskazov and R. Studdert
Index.

Subject Areas: Miscellaneous items [WZ]