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＜電子ブック＞
Theory and Applications of Partial Functional Differential Equations / by Jianhong Wu
(Applied Mathematical Sciences. ISSN:2196968X ; 119)

版	1st ed. 1996.
出版者	New York, NY : Springer New York : Imprint: Springer
出版年	1996
本文言語	英語
大きさ	X, 432 p : online resource
冊子体	Theory and applications of partial functional differential equations / Jianhong Wu
著者標目	*Wu, Jianhong author SpringerLink (Online service)
件　名	LCSH:Mathematical analysis LCSH:Manifolds (Mathematics) FREE:Analysis FREE:Manifolds and Cell Complexes
一般注記	1. Preliminaries -- 1.1 Semigroups and generators -- 1.2 Function spaces, elliptic operators, and maximal principles -- Bibliographical Notes -- 2. Existence and Compactness of Solution Semiflows -- 2.1 Existence and compactness -- 2.2 Local existence and global continuation -- 2.3 Extensions to neutral partial functional differential equations -- Bibliographical Notes -- 3. Generators and Decomposition of State Spaces for Linear Systems -- 3.1 Infinitesimal generators of solution semiflows of linear systems -- 3.2 Decomposition of state spaces by invariant subspaces -- 3.3 Computation of center, stable, and unstable subspaces -- 3.4 Extensions to equations with infinite delay -- 3.5 L2-stability and reduction of neutral equations -- Bibliographical Notes -- 4. Nonhomogeneous Systems and Linearized Stability -- 4.1 Dual operators and an alternative theorem -- 4.2 Variation of constants formula -- 4.3 Existence of periodic or almost periodic solutions -- 4.4 Principle of linearized stability -- 4.5 Fundamental transformations and representations of solutions -- Bibliographical Notes -- 5. Invariant Manifolds of Nonlinear Systems -- 5.1 Stable and unstable manifolds -- 5.2 Center manifolds -- 5.3 Flows on center manifolds -- 5.4 Global invariant manifolds of perturbed wave equations -- Bibliographical Notes -- 6. Hopf Bifurcations -- 6.1 Some classical Hopf bifurcation theorems for ODEs -- 6.2 Smooth local Hopf bifurcations: a special case -- 6.3 Some examples from population dynamics -- 6.4 Smooth local Hopf bifurcations: general situations -- 6.5 A topological global Hopf bifurcation theory -- 6.6 Global continuation of wave solutions -- Bibliographical Notes -- 7. Small and Large Diffusivity -- 7.1 Destablization of periodic solutions by small diffusivity -- 7.2 Large diffusivity under Neumann boundary conditions -- Bibliographical Notes -- 8. Invariance, Comparison, and Upper and Lower Solutions -- 8.1 Invariance and inequalities -- 8.2 Systems and strict inequalities -- 8.3 Applications to reaction diffusion equations with delay -- Bibliographical Notes -- 9. Convergence, Monotonicity, and Contracting Rectangles -- 9.1 Monotonicity and generic convergence -- 9.2 Stability and steady state solutions of quasimonotone systems -- 9.3 Comparison and convergence results -- 9.4 Applications to Lotka-Volterra competition models -- Bibliographical Notes -- 10. Dispativeness, Exponential Growth, and Invariance Principles -- 10.1 Point dispativeness in a scalar equation -- 10.2 Convergence in a scalar equation -- 10.3 Exponential growth in a scalar equation -- 10.4 An invariance principle -- Bibliographical Notes -- 11. Traveling Wave Solutions -- 11.1 Huxley nonlinearities and phase plane arguments -- 11.2 Delayed Fisher equation: sub-super solution method -- 11.3 Systems and monotone iteration method -- 11.4 Traveling oscillatory waves -- Bibliographical Notes Abstract semilinear functional differential equations arise from many biological, chemical, and physical systems which are characterized by both spatial and temporal variables and exhibit various spatio-temporal patterns. The aim of this book is to provide an introduction of the qualitative theory and applications of these equations from the dynamical systems point of view. The required prerequisites for that book are at a level of a graduate student. The style of presentation will be appealing to people trained and interested in qualitative theory of ordinary and functional differential equations Accessibility summary: This PDF is not accessible. It is based on scanned pages and does not support features such as screen reader compatibility or described non-text content (images, graphs etc). However, it likely supports searchable and selectable text based on OCR (Optical Character Recognition). Users with accessibility needs may not be able to use this content effectively. Please contact us at accessibilitysupport@springernature.com if you require assistance or an alternative format Inaccessible, or known limited accessibility No reading system accessibility options actively disabled Publisher contact for further accessibility information: accessibilitysupport@springernature.com HTTP:URL=https://doi.org/10.1007/978-1-4612-4050-1

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