A Study Of Heteroclinic Orbits For A Class Of Fourth Order Ordinary Differential Equations
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A Study Of Heteroclinic Orbits For A Class Of Fourth Order Ordinary Differential Equations
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Author : Denis Bonheure
language : en
Publisher: Presses univ. de Louvain
Release Date : 2004
A Study Of Heteroclinic Orbits For A Class Of Fourth Order Ordinary Differential Equations written by Denis Bonheure and has been published by Presses univ. de Louvain this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004 with Science categories.
In qualitative theory of differential equations, an important role is played by special classes of solutions, like periodic solutions or solutions to some boundary value problems. When a system of ordinary differential equations has equilibria, i.e. constant solutions, whose stability properties are known, it is significant to search for connections between them by trajectories of solutions of the given system. These are called homoclinic or heteroclinic, according to whether they describe a loop based at one single equilibrium or they "start" and "end" at two distinct equilibria. This thesis is devoted to the study of heteroclinic solutions for a specific class of ordinary differential equations related to the Extended Fisher-Kolmogorov equation and the Swift-Hohenberg equation. These are semilinear fourth order bi-stable evolution equations which appear as mathematical models for problems arising in Mechanics, Chemistry and Biology. For such equations, the set of bounded stationary solutions is of great interest. These solve an autonomous fourth order equation. In this thesis, we focus on such equations having a variational structure. In that case, the solutions are critical points of an associated action functional defined in convenient functional spaces. We then look for heteroclinic solutions as minimizers of the action functional. Our main contributions concern existence and multiplicity results of such global and local minimizers in the case where the functional is defined from sign changing Lagrangians. The underlying idea is to impose conditions which imply a lower bound on the action over all admissible functions. We then combine classical arguments of the Calculus of Variations with careful estimates on minimizing sequences to prove the existence of a minimum.
Handbook Of Differential Equations Ordinary Differential Equations
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Author : A. Canada
language : en
Publisher: Elsevier
Release Date : 2006-08-21
Handbook Of Differential Equations Ordinary Differential Equations written by A. Canada and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-21 with Mathematics categories.
This handbook is the third volume in a series of volumes devoted to self contained and up-to-date surveys in the tehory of ordinary differential equations, written by leading researchers in the area. All contributors have made an additional effort to achieve readability for mathematicians and scientists from other related fields so that the chapters have been made accessible to a wide audience. These ideas faithfully reflect the spirit of this multi-volume and hopefully it becomes a very useful tool for reseach, learing and teaching. This volumes consists of seven chapters covering a variety of problems in ordinary differential equations. Both pure mathematical research and real word applications are reflected by the contributions to this volume. Covers a variety of problems in ordinary differential equations Pure mathematical and real world applications Written for mathematicians and scientists of many related fields
Heteroclinic Solutions For A Class Of Fourth Order Ordinary Differential Equations
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Author : Denis Bonheure
language : en
Publisher:
Release Date : 2006
Heteroclinic Solutions For A Class Of Fourth Order Ordinary Differential Equations written by Denis Bonheure and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006 with Differential equations categories.
Homoclinic And Heteroclinic Orbits For A Class Of 4 Dimensional Hamiltonian Systems
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Author : Konstantin Michael Mischaikow
language : en
Publisher:
Release Date : 1985
Homoclinic And Heteroclinic Orbits For A Class Of 4 Dimensional Hamiltonian Systems written by Konstantin Michael Mischaikow and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with categories.
New Trends In Differential And Difference Equations And Applications
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Author : Feliz Manuel Minhós
language : en
Publisher: MDPI
Release Date : 2019-10-14
New Trends In Differential And Difference Equations And Applications written by Feliz Manuel Minhós and has been published by MDPI this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-10-14 with Mathematics categories.
This Special Issue aims to be a compilation of new results in the areas of differential and difference Equations, covering boundary value problems, systems of differential and difference equations, as well as analytical and numerical methods. The objective is to provide an overview of techniques used in these different areas and to emphasize their applicability to real-life phenomena, by the inclusion of examples. These examples not only clarify the theoretical results presented, but also provide insight on how to apply, for future works, the techniques used.
Applied Mechanics Reviews
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Author :
language : en
Publisher:
Release Date : 1991
Applied Mechanics Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1991 with Mechanics, Applied categories.
Mathematical Reviews
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Author :
language : en
Publisher:
Release Date : 2007
Mathematical Reviews written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Mathematics categories.
Methods Of Qualitative Theory Of Differential Equations And Related Topics
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Author : Lev M. Lerman
language : en
Publisher: American Mathematical Soc.
Release Date : 2000
Methods Of Qualitative Theory Of Differential Equations And Related Topics written by Lev M. Lerman and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000 with Mathematics categories.
Dedicated to the memory of Professor E. A. Leontovich-Andronova, this book was composed by former students and colleagues who wished to mark her contributions to the theory of dynamical systems. A detailed introduction by Leontovich-Andronova's close colleague, L. Shilnikov, presents biographical data and describes her main contribution to the theory of bifurcations and dynamical systems. The main part of the volume is composed of research papers presenting the interests of Leontovich-Andronova, her students and her colleagues. Included are articles on traveling waves in coupled circle maps, bifurcations near a homoclinic orbit, polynomial quadratic systems on the plane, foliations on surfaces, homoclinic bifurcations in concrete systems, topology of plane controllability regions, separatrix cycle with two saddle-foci, dynamics of 4-dimensional symplectic maps, torus maps from strong resonances, structure of 3 degree-of-freedom integrable Hamiltonian systems, splitting separatrices in complex differential equations, Shilnikov's bifurcation for C1-smooth systems and "blue sky catastrophe" for periodic orbits.
Nonlinear Optics
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Author : Alan Newell
language : en
Publisher: CRC Press
Release Date : 2018-05-04
Nonlinear Optics written by Alan Newell and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-05-04 with Science categories.
This book is about Nonlinear Optics, the study of how high-intensity light propagates through and interacts with matter. It takes the reader from the starting point of Maxwell's equations to some of the frontiers of modern research in the subject.
Accurate Computation And Continuation Of Homoclinic And Heteroclinic Orbits For Singular Perturbation Problems
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Author :
language : en
Publisher:
Release Date : 1993
Accurate Computation And Continuation Of Homoclinic And Heteroclinic Orbits For Singular Perturbation Problems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.