Brings together many important recent developments in the analysis of singular perturbation and hysteresis phenomena in an accessible and comprehensive fashion. To bridge a gap between analysts of these phenomena, the editors conducted a workshop in April 2002 at University College Cork in Ireland to provide a forum for experts in both fields 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. The book begins with a basic introduction to hysteresis and singular perturbation theory, including 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. The geometrical approach to an investigation of models with singular perturbations and hysteresis. The editors expect this text not only to be a useful and accessible introduction to techniques and the research literature but also to generate new ideas for researchers and to attract new researchers into this vibrant and dynamic field.
Michael P. Mortell is President Emeritus and Professor of Applied Mathematics at University College Cork, Ireland. Robert E. O'Malley is Professor of Applied Mathematics at the University of Washington, Seattle, USA. Alexei Pokrovskii is Professor of Applied Mathematics at University College Cork, Ireland. Vladimir Sobolev is Professor of Differential Equations and Control Theory at Samara State University, Russia.
List of Contributors Preface Chapter 1: A Naive View of Time Relaxation and Hysteresis, A. Pokrovskii, V. Sobolev Chapter 2: Frustration Minimization, Hysteresis and the El Farol Problem, R. Cross, M. Grinfeld, H. Lamba, A. Pittock Chapter 3: Hysteresis in Singularly Perturbed Problems, P. Krej?i Chapter 4: Combined Asymptotic Expansions, E. Benoit, A. Fruchard, A. El Hamidi Chapter 5: Contrast Structures of Alternating Type, A. Vasilieva Chapter 6: Multi-Dimensional Internal Layers, N. Nefedov Chapter 7: Geometry of Singular Perturbations: Critical Cases, V. Sobolev Chapter 8: Black Swans and Canards in Laser and Combustion Models, E. Shchepakina, V. Sobolev Chapter 9: Multi-Scale Analysis of Pressure Driven Flames, V. Bykov, I. Goldfarb, V. Gol'dshtein Chapter 10: Split-Hyperbolicity, Hysteresis and Lang-Kobayashi Equations, A. Pokrovskii, O. Rasskazov, R. Studdert Index.
