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Dynamics Reported : Expositions in Dynamical Systems New Series: Volume 3
(Dynamics Reported. New Series, Expositions in Dynamical Systems. ISSN:29428548 ; 3)

版	1st ed. 1994.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	1994
本文言語	英語
大きさ	VIII, 162 p : online resource
著者標目	SpringerLink (Online service)
件　名	LCSH:Algebraic topology LCSH:Mathematical analysis LCSH:Biomathematics LCSH:Mathematical physics FREE:Algebraic Topology FREE:Analysis FREE:Mathematical and Computational Biology FREE:Theoretical, Mathematical and Computational Physics
一般注記	Limit Relative Category and Critical Point Theory -- 1. Introduction -- 2. Relative Category -- 3. Relative Cuplength -- 4. Limit Relative Category -- 5. The Deformation Lemma -- 6. Critical Point Theorems -- 7. Some Applications -- 8. A Perturbation Theorem -- References -- Coexistence of Infinitely Many Stable Solutions to Reaction Diffusion Systems in the Singular Limit -- 1. Introduction and singular limit slow dynamics -- 2. Intuitive Approach to the Stability of Multi-layered Solutions -- 3. The SLEP Method for the Stability of Normal N-layered Solutions -- 4. Recovery Process of Stability -- 5. Concluding Remarks -- Appendix A -- Appendix B -- Appendix C -- References -- Recent advances in regularity of second-order hyperbolic mixed problems, and applications -- 1. Introduction -- I: Regularity Theory -- 2. Regularity under Dirichlet boundary conditions -- 3. Regularity under Neumann Boundary Conditions -- 4. Cosine/Sine (Semigroup) Representation Formulae of the Solutions -- II: Applications -- 5. Well-posedness of Semi-linear Wave Equations with Neumann Boundary Conditions -- 6. Local Exponential Stability of Damped Wave Equations with Semi-linear Boundary Conditions -- 7. Exact Controllability of Semi-linear Hyperbolic Problems -- 8. Riccati Operator Equations and Hyperbolic Mixed Problems -- References DYNAMICS REPORTED reports on recent developments in dynamical systems. Dynamical systems of course originated from ordinary differential equations. Today, dynamical systems cover a much larger area, including dynamical processes described by functional and integral equations, by partial and stochastic differential equations, etc. Dynamical systems have involved remarkably in recent years. A wealth of new phenomena, new ideas and new techniques are proving to be of considerable interest to scientists in rather different fields. It is not surprising that thousands of publications on the theory itself and on its various applications are appearing DYNAMICS REPORTED presents carefully written articles on major subjects in dynamical systems and their applications, addressed not only to specialists but also to a broader range of readers including graduate students. Topics are advanced, while detailed exposition of ideas, restriction to typical results - rather than the most general one- and, last but not least, lucid proofs help to gain the utmost degree of clarity. It is hoped, that DYNAMICS REPORTED will be useful for those entering the field and will stimulate an exchange of ideas among those working in dynamical systems Summer 1991 Christopher K. R. T Jones Drs Kirchgraber Hans-Otto Walther Managing Editors Table of Contents Limit Relative Category and Critical Point Theory G. Fournier, D. Lupo, M. Ramos, M. Willem 1. Introduction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 2. Relative Category . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 3. Relative Cupiength . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . 6 4. Limit Relative Category . . . . . . . . . . . . . . . . . . . . . . . '" . . . . " . . . . . . . . . . . . . . . . 10 5. The Deformation Lemma . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 6. Critical Point Theorems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13 7. Some Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . HTTP:URL=https://doi.org/10.1007/978-3-642-78234-3

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