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Dynamics Of Partial Differential Equations
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Book Synopsis Effective Dynamics of Stochastic Partial Differential Equations by : Jinqiao Duan
Download or read book Effective Dynamics of Stochastic Partial Differential Equations written by Jinqiao Duan and published by Elsevier. This book was released on 2014-03-06 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: Effective Dynamics of Stochastic Partial Differential Equations focuses on stochastic partial differential equations with slow and fast time scales, or large and small spatial scales. The authors have developed basic techniques, such as averaging, slow manifolds, and homogenization, to extract effective dynamics from these stochastic partial differential equations. The authors' experience both as researchers and teachers enable them to convert current research on extracting effective dynamics of stochastic partial differential equations into concise and comprehensive chapters. The book helps readers by providing an accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations. Each chapter also includes exercises and problems to enhance comprehension. - New techniques for extracting effective dynamics of infinite dimensional dynamical systems under uncertainty - Accessible introduction to probability tools in Hilbert space and basics of stochastic partial differential equations - Solutions or hints to all Exercises
Download or read book Nonlinear PDEs written by Guido Schneider and published by American Mathematical Soc.. This book was released on 2017-10-26 with total page 593 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an introductory textbook about nonlinear dynamics of PDEs, with a focus on problems over unbounded domains and modulation equations. The presentation is example-oriented, and new mathematical tools are developed step by step, giving insight into some important classes of nonlinear PDEs and nonlinear dynamics phenomena which may occur in PDEs. The book consists of four parts. Parts I and II are introductions to finite- and infinite-dimensional dynamics defined by ODEs and by PDEs over bounded domains, respectively, including the basics of bifurcation and attractor theory. Part III introduces PDEs on the real line, including the Korteweg-de Vries equation, the Nonlinear Schrödinger equation and the Ginzburg-Landau equation. These examples often occur as simplest possible models, namely as amplitude or modulation equations, for some real world phenomena such as nonlinear waves and pattern formation. Part IV explores in more detail the connections between such complicated physical systems and the reduced models. For many models, a mathematically rigorous justification by approximation results is given. The parts of the book are kept as self-contained as possible. The book is suitable for self-study, and there are various possibilities to build one- or two-semester courses from the book.
Book Synopsis Dynamics of Partial Differential Equations by : C. Eugene Wayne
Download or read book Dynamics of Partial Differential Equations written by C. Eugene Wayne and published by Springer. This book was released on 2015-08-08 with total page 90 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains two review articles on the dynamics of partial differential equations that deal with closely related topics but can be read independently. Wayne reviews recent results on the global dynamics of the two-dimensional Navier-Stokes equations. This system exhibits stable vortex solutions: the topic of Wayne's contribution is how solutions that start from arbitrary initial conditions evolve towards stable vortices. Weinstein considers the dynamics of localized states in nonlinear Schrodinger and Gross-Pitaevskii equations that describe many optical and quantum systems. In this contribution, Weinstein reviews recent bifurcations results of solitary waves, their linear and nonlinear stability properties and results about radiation damping where waves lose energy through radiation. The articles, written independently, are combined into one volume to showcase the tools of dynamical systems theory at work in explaining qualitative phenomena associated with two classes of partial differential equations with very different physical origins and mathematical properties.
Download or read book PDE Dynamics written by Christian Kuehn and published by SIAM. This book was released on 2019-04-10 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an overview of the myriad methods for applying dynamical systems techniques to PDEs and highlights the impact of PDE methods on dynamical systems. Also included are many nonlinear evolution equations, which have been benchmark models across the sciences, and examples and techniques to strengthen preparation for research. PDE Dynamics: An Introduction is intended for senior undergraduate students, beginning graduate students, and researchers in applied mathematics, theoretical physics, and adjacent disciplines. Structured as a textbook or seminar reference, it can be used in courses titled Dynamics of PDEs, PDEs 2, Dynamical Systems 2, Evolution Equations, or Infinite-Dimensional Dynamics.
Author :Victor A. Galaktionov Publisher :Springer Science & Business Media ISBN 13 :1461220505 Total Pages :388 pages Book Rating :4.4/5 (612 download)
Book Synopsis A Stability Technique for Evolution Partial Differential Equations by : Victor A. Galaktionov
Download or read book A Stability Technique for Evolution Partial Differential Equations written by Victor A. Galaktionov and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: * Introduces a state-of-the-art method for the study of the asymptotic behavior of solutions to evolution partial differential equations. * Written by established mathematicians at the forefront of their field, this blend of delicate analysis and broad application is ideal for a course or seminar in asymptotic analysis and nonlinear PDEs. * Well-organized text with detailed index and bibliography, suitable as a course text or reference volume.
Book Synopsis Ordinary Differential Equations and Dynamical Systems by : Gerald Teschl
Download or read book Ordinary Differential Equations and Dynamical Systems written by Gerald Teschl and published by American Mathematical Soc.. This book was released on 2012-08-30 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained introduction to ordinary differential equations and dynamical systems suitable for beginning graduate students. The first part begins with some simple examples of explicitly solvable equations and a first glance at qualitative methods. Then the fundamental results concerning the initial value problem are proved: existence, uniqueness, extensibility, dependence on initial conditions. Furthermore, linear equations are considered, including the Floquet theorem, and some perturbation results. As somewhat independent topics, the Frobenius method for linear equations in the complex domain is established and Sturm-Liouville boundary value problems, including oscillation theory, are investigated. The second part introduces the concept of a dynamical system. The Poincare-Bendixson theorem is proved, and several examples of planar systems from classical mechanics, ecology, and electrical engineering are investigated. Moreover, attractors, Hamiltonian systems, the KAM theorem, and periodic solutions are discussed. Finally, stability is studied, including the stable manifold and the Hartman-Grobman theorem for both continuous and discrete systems. The third part introduces chaos, beginning with the basics for iterated interval maps and ending with the Smale-Birkhoff theorem and the Melnikov method for homoclinic orbits. The text contains almost three hundred exercises. Additionally, the use of mathematical software systems is incorporated throughout, showing how they can help in the study of differential equations.
Book Synopsis Nonlinear Dynamics in Partial Differential Equations by : Shin-Ichiro Ei
Download or read book Nonlinear Dynamics in Partial Differential Equations written by Shin-Ichiro Ei and published by . This book was released on 2018 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Ordinary Differential Equations and Dynamical Systems by : Thomas C. Sideris
Download or read book Ordinary Differential Equations and Dynamical Systems written by Thomas C. Sideris and published by Springer Science & Business Media. This book was released on 2013-10-17 with total page 230 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a mathematically rigorous introduction to the beautiful subject of ordinary differential equations for beginning graduate or advanced undergraduate students. Students should have a solid background in analysis and linear algebra. The presentation emphasizes commonly used techniques without necessarily striving for completeness or for the treatment of a large number of topics. The first half of the book is devoted to the development of the basic theory: linear systems, existence and uniqueness of solutions to the initial value problem, flows, stability, and smooth dependence of solutions upon initial conditions and parameters. Much of this theory also serves as the paradigm for evolutionary partial differential equations. The second half of the book is devoted to geometric theory: topological conjugacy, invariant manifolds, existence and stability of periodic solutions, bifurcations, normal forms, and the existence of transverse homoclinic points and their link to chaotic dynamics. A common thread throughout the second part is the use of the implicit function theorem in Banach space. Chapter 5, devoted to this topic, the serves as the bridge between the two halves of the book.
Book Synopsis Partial Differential Equations by : Walter A. Strauss
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Book Synopsis Partial Differential Equations and Dynamical Systems by : William Edward Fitzgibbon
Download or read book Partial Differential Equations and Dynamical Systems written by William Edward Fitzgibbon and published by Pitman Advanced Publishing Program. This book was released on 1984 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: There has recently been a great amount of activity and a rapid growth in the areas of partial differential equations and dynamical systems. This interest has been encouraged by the development of powerful new techniques in nonlinear analysis and a renewed scientific interest in applied mathematical analysis. This book has been designed to make the reader aware of progress and current problems in this exciting and useful area. The book consists of articles by internationally known mathematical scientists, based on lectures given during a year-long program at the University of Houston.
Book Synopsis Partial Differential Equations in Classical Mathematical Physics by : Isaak Rubinstein
Download or read book Partial Differential Equations in Classical Mathematical Physics written by Isaak Rubinstein and published by Cambridge University Press. This book was released on 1998-04-28 with total page 704 pages. Available in PDF, EPUB and Kindle. Book excerpt: The unique feature of this book is that it considers the theory of partial differential equations in mathematical physics as the language of continuous processes, that is, as an interdisciplinary science that treats the hierarchy of mathematical phenomena as reflections of their physical counterparts. Special attention is drawn to tracing the development of these mathematical phenomena in different natural sciences, with examples drawn from continuum mechanics, electrodynamics, transport phenomena, thermodynamics, and chemical kinetics. At the same time, the authors trace the interrelation between the different types of problems - elliptic, parabolic, and hyperbolic - as the mathematical counterparts of stationary and evolutionary processes. This combination of mathematical comprehensiveness and natural scientific motivation represents a step forward in the presentation of the classical theory of PDEs, one that will be appreciated by both students and researchers alike.
Book Synopsis Partial Differential Equations and Fluid Mechanics by : James C. Robinson
Download or read book Partial Differential Equations and Fluid Mechanics written by James C. Robinson and published by Cambridge University Press. This book was released on 2009-07-16 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Reviews and research articles summarizing a wide range of active research topics in fluid mechanics.
Book Synopsis Differential Equations and Dynamical Systems by : D. Bahuguna
Download or read book Differential Equations and Dynamical Systems written by D. Bahuguna and published by Alpha Science Int'l Ltd.. This book was released on 2005 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fifteen chapters from eminent researchers working in the area of differential equations and dynamical systems covering all relevant subjects, ranging from wavelets and their applications, to second order evolution equations.
Book Synopsis Partial Differential Equations in Ecology by : Sergei Petrovski
Download or read book Partial Differential Equations in Ecology written by Sergei Petrovski and published by MDPI. This book was released on 2021-03-17 with total page 238 pages. Available in PDF, EPUB and Kindle. Book excerpt: Partial differential equations (PDEs) have been used in theoretical ecology research for more than eighty years. Nowadays, along with a variety of different mathematical techniques, they remain as an efficient, widely used modelling framework; as a matter of fact, the range of PDE applications has even become broader. This volume presents a collection of case studies where applications range from bacterial systems to population dynamics of human riots.
Book Synopsis Random Perturbation of PDEs and Fluid Dynamic Models by : Franco Flandoli
Download or read book Random Perturbation of PDEs and Fluid Dynamic Models written by Franco Flandoli and published by Springer Science & Business Media. This book was released on 2011-03-11 with total page 187 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume explores the random perturbation of PDEs and fluid dynamic models. The text describes the role of additive and bilinear multiplicative noise, and includes examples of abstract parabolic evolution equations.
Book Synopsis Partial Differential Equations in Mechanics 1 by : A.P.S. Selvadurai
Download or read book Partial Differential Equations in Mechanics 1 written by A.P.S. Selvadurai and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 610 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume work focuses on partial differential equations (PDEs) with important applications in mechanical and civil engineering, emphasizing mathematical correctness, analysis, and verification of solutions. The presentation involves a discussion of relevant PDE applications, its derivation, and the formulation of consistent boundary conditions.
