Download or read book Nonlinear Systems Of Partial Differential Equations Applications To Life And Physical Sciences written by Anthony W Leung and published by World Scientific. This book was released on 2009-08-28 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the theory of diffusion-reaction equations starting from the Volterra-Lotka systems developed in the eighties for Dirichlet boundary conditions. It uses the analysis of applicable systems of partial differential equations as a starting point for studying upper-lower solutions, bifurcation, degree theory and other nonlinear methods. It also illustrates the use of semigroup, stability theorems and W2ptheory. Introductory explanations are included in the appendices for non-expert readers.The first chapter covers a wide range of steady-state and stability results involving prey-predator, competing and cooperating species under strong or weak interactions. Many diagrams are included to easily understand the description of the range of parameters for coexistence. The book provides a comprehensive presentation of topics developed by numerous researchers. Large complex systems are introduced for modern research in ecology, medicine and engineering.Chapter 3 combines the theories of earlier chapters with the optimal control of systems involving resource management and fission reactors. This is the first book to present such topics at research level. Chapter 4 considers persistence, cross-diffusion, and boundary induced blow-up, etc. The book also covers traveling or systems of waves, coupled Navier-Stokes and Maxwell systems, and fluid equations of plasma display. These should be of interest to life and physical scientists.
Download or read book An Introduction to Nonlinear Partial Differential Equations written by J. David Logan and published by John Wiley & Sons. This book was released on 2008-04-11 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: Praise for the First Edition: "This book is well conceived and well written. The author has succeeded in producing a text on nonlinear PDEs that is not only quite readable but also accessible to students from diverse backgrounds." —SIAM Review A practical introduction to nonlinear PDEs and their real-world applications Now in a Second Edition, this popular book on nonlinear partial differential equations (PDEs) contains expanded coverage on the central topics of applied mathematics in an elementary, highly readable format and is accessible to students and researchers in the field of pure and applied mathematics. This book provides a new focus on the increasing use of mathematical applications in the life sciences, while also addressing key topics such as linear PDEs, first-order nonlinear PDEs, classical and weak solutions, shocks, hyperbolic systems, nonlinear diffusion, and elliptic equations. Unlike comparable books that typically only use formal proofs and theory to demonstrate results, An Introduction to Nonlinear Partial Differential Equations, Second Edition takes a more practical approach to nonlinear PDEs by emphasizing how the results are used, why they are important, and how they are applied to real problems. The intertwining relationship between mathematics and physical phenomena is discovered using detailed examples of applications across various areas such as biology, combustion, traffic flow, heat transfer, fluid mechanics, quantum mechanics, and the chemical reactor theory. New features of the Second Edition also include: Additional intermediate-level exercises that facilitate the development of advanced problem-solving skills New applications in the biological sciences, including age-structure, pattern formation, and the propagation of diseases An expanded bibliography that facilitates further investigation into specialized topics With individual, self-contained chapters and a broad scope of coverage that offers instructors the flexibility to design courses to meet specific objectives, An Introduction to Nonlinear Partial Differential Equations, Second Edition is an ideal text for applied mathematics courses at the upper-undergraduate and graduate levels. It also serves as a valuable resource for researchers and professionals in the fields of mathematics, biology, engineering, and physics who would like to further their knowledge of PDEs.
Download or read book Systems of Nonlinear Partial Differential Equations written by A.W. Leung and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: 'Et moi ..., si j'avait su comment en reveru.r, One service mathematics has rendered the je n'y scrais point aIle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled 'discarded non The series is divergent; therefore we may be sense'. Eric T. Bell able to do something with it. o. Heaviside Mathematics is a tool for thought. A highly necessary tool in a world where both feedback and non linearities abound. Similarly, all kinds of parts of mathematics serve as tools for other parts and for other sciences. Applying a simple rewriting rule to the quote on the right above one finds such statements as: 'One service topology has rendered mathematical physics .. .'; 'One service logic has rendered com puter science .. .'; 'One service category theory has rendered mathematics .. .'. All arguably true. And all statements obtainable this way form part of the raison d'etre of this series.
Download or read book Systems of Nonlinear Partial Differential Equations written by J.M. Ball and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains the proceedings of a NATO/London Mathematical Society Advanced Study Institute held in Oxford from 25 July - 7 August 1982. The institute concerned the theory and applications of systems of nonlinear partial differential equations, with emphasis on techniques appropriate to systems of more than one equation. Most of the lecturers and participants were analysts specializing in partial differential equations, but also present were a number of numerical analysts, workers in mechanics, and other applied mathematicians. The organizing committee for the institute was J.M. Ball (Heriot-Watt), T.B. Benjamin (Oxford), J. Carr (Heriot-Watt), C.M. Dafermos (Brown), S. Hildebrandt (Bonn) and J.S. pym (Sheffield) . The programme of the institute consisted of a number of courses of expository lectures, together with special sessions on different topics. It is a pleasure to thank all the lecturers for the care they took in the preparation of their talks, and S.S. Antman, A.J. Chorin, J.K. Hale and J.E. Marsden for the organization of their special sessions. The institute was made possible by financial support from NATO, the London Mathematical Society, the u.S. Army Research Office, the u.S. Army European Research Office, and the u.S. National Science Foundation. The lectures were held in the Mathematical Institute of the University of Oxford, and residential accommodation was provided at Hertford College.
Download or read book Nonlinear Systems written by Christos K. Volos and published by Nova Science Publishers. This book was released on 2017 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: A nonlinear system is a set of nonlinear equations, which may be algebraic, ordinary differential, partial differential, fractional, integral or a combination of these. Especially, nowadays, the term "dynamical system" is used as a synonym of nonlinear systems where the nonlinear equations represent the evolution of a solution over time. So, the notion of dynamical systems arose following the name of equations governing the motion of a system of particles, even though the nonlinear system may have no application to mechanics. Also, from an engineering point of view a nonlinear system may be represented with a feedback loop in which the output of an element is not proportional to its input. Over the last few decades, nonlinear systems have been used to describe a great variety of phenomena, in social and life sciences as well as in physical sciences and engineering. The theory of nonlinear systems has applications to problems of population growth, economics, chemical reactions, celestial mechanics, physiology of nerves, onset of turbulence, regulation of heartbeats, electronic circuits, cryptography, secure communications and many others. Nonlinear dynamical systems, which present chaotic behavior, are of great importance due to their applications in science and engineering. Chaotic systems are nonlinear dynamical systems and maps that are highly sensitive to initial conditions. The sensitivity of initial conditions is usually called the butter'y effect for dynamical systems and maps. So, nowadays the design and analysis of nonlinear systems and especially chaotic systems has gained the interest of the research community due to the fact that many phenomena on financial, physical, biological, chemical, mechanical and engineering systems can be modeled and studied through the perspective of nonlinear dynamics. These nonlinear systems can be modeled by discrete-time or continuous-time mathematical models.This book aims to bridge the gap between the design/analysis and applications, which are the two research stages on the progress of nonlinear systems and also which open up some new directions of real applications, where chaos can be put up to technological use, including secure communication systems, electronic circuits' design, memristors and radar. Finally, this book can serve as an updated and handy reference for university professors, graduate students, laboratory researchers as well as physicists and applied mathematicians who are interested in studying the chaos and its applications through the field of nonlinear systems.
Download or read book Nonlinear Partial Differential Equations for Scientists and Engineers written by Lokenath Debnath and published by Springer Science & Business Media. This book was released on 2011-10-06 with total page 872 pages. Available in PDF, EPUB and Kindle. Book excerpt: The revised and enlarged third edition of this successful book presents a comprehensive and systematic treatment of linear and nonlinear partial differential equations and their varied and updated applications. In an effort to make the book more useful for a diverse readership, updated modern examples of applications are chosen from areas of fluid dynamics, gas dynamics, plasma physics, nonlinear dynamics, quantum mechanics, nonlinear optics, acoustics, and wave propagation. Nonlinear Partial Differential Equations for Scientists and Engineers, Third Edition, improves on an already highly complete and accessible resource for graduate students and professionals in mathematics, physics, science, and engineering. It may be used to great effect as a course textbook, research reference, or self-study guide.
Download or read book Dispersive Partial Differential Equations written by M. Burak Erdoğan and published by Cambridge University Press. This book was released on 2016-05-03 with total page 203 pages. Available in PDF, EPUB and Kindle. Book excerpt: The area of nonlinear dispersive partial differential equations (PDEs) is a fast developing field which has become exceedingly technical in recent years. With this book, the authors provide a self-contained and accessible introduction for graduate or advanced undergraduate students in mathematics, engineering, and the physical sciences. Both classical and modern methods used in the field are described in detail, concentrating on the model cases that simplify the presentation without compromising the deep technical aspects of the theory, thus allowing students to learn the material in a short period of time. This book is appropriate both for self-study by students with a background in analysis, and for teaching a semester-long introductory graduate course in nonlinear dispersive PDEs. Copious exercises are included, and applications of the theory are also presented to connect dispersive PDEs with the more general areas of dynamical systems and mathematical physics.
Download or read book Physical Mathematics and Nonlinear Partial Differential Equations written by Lightbourne and published by CRC Press. This book was released on 2020-12-17 with total page 281 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume consists of the proceedings of the conference on Physical Mathematics and Nonlinear Partial Differential Equations held at West Virginia University in Morgantown. It describes some work dealing with weak limits of solutions to nonlinear systems of partial differential equations.
Download or read book Nonlinear Partial Differential Equations And Applications Proceedings Of The Conference written by Boling Guo and published by World Scientific. This book was released on 1998-10-30 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: Contents: Direct and Inverse Diffraction by Periodic Structures (G Bao)Weak Flow of H-Systems (Y-M Chen)Strongly Compact Attractor for Dissipative Zakharov Equations (B-L Guo et al.)C∞-Solutions of Generalized Porous Medium Equations (M Ôtani & Y Sugiyama)Cauchy Problem for Generalized IMBq Equation (G-W Chen & S-B Wang)Inertial Manifolds for a Nonlocal Kuramoto–Sivashinsky Equation (J-Q Duan et al.)Weak Solutions of the Generalized Magnetic Flow Equations (S-H He & Z-D Dai)The Solution of Hammerstein Integral Equation Without Coercive Conditions (Y-L Shu)Global Behaviour of the Solution of Nonlinear Forest Evolution Equation (D-J Wang)Uniqueness of Generalized Solutions for Semiconductor Equations (J-S Xing & Y Hu)On the Vectorial Hamilton–Jacobi System (B-S Yan)An Integrable Hamiltonian System Associated with cKdV Hierarchy (J-S Zhang et al.)and other papers Readership: Mathematicians. Keywords:Diffraction;Weak Flow;Zakharov Equations;Porous Medium Equations;Cauchy Problem;IMBq Equation;Kuramoto-Sivashinsky Equation;Magnetic Flow Equations;Hammerstein Integral Equation;Nonlinear Forest Evolution Equation;Uniqueness;Generalized Solutions;Semiconductor Equations;HamiltonâJacobi System;Hamiltonian System;cKdV Hierarchy
Download or read book Nonlinear Partial Differential Equations in Geometry and Physics written by Garth Baker and published by Birkhäuser. This book was released on 2012-12-06 with total page 166 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the proceedings of a series of lectures hosted by the Math ematics Department of The University of Tennessee, Knoxville, March 22-24, 1995, under the title "Nonlinear Partial Differential Equations in Geometry and Physics" . While the relevance of partial differential equations to problems in differen tial geometry has been recognized since the early days of the latter subject, the idea that differential equations of differential-geometric origin can be useful in the formulation of physical theories is a much more recent one. Perhaps the earliest emergence of systems of nonlinear partial differential equations having deep geo metric and physical importance were the Einstein equations of general relativity (1915). Several basic aspects of the initial value problem for the Einstein equa tions, such as existence, regularity and stability of solutions remain prime research areas today. eighty years after Einstein's work. An even more recent development is the realization that structures originally the context of models in theoretical physics may turn out to have introduced in important geometric or topological applications. Perhaps its emergence can be traced back to 1954, with the introduction of a non-abelian version of Maxwell's equations as a model in elementary-particle physics, by the physicists C.N. Yang and R. Mills. The rich geometric structure ofthe Yang-Mills equations was brought to the attention of mathematicians through work of M.F. Atiyah, :"J. Hitchin, I.
Download or read book Systems of Nonlinear Partial Differential Equations written by Anthony Leung and published by Springer. This book was released on 2014-03-14 with total page 409 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear PDEs written by Marius Ghergu and published by Springer Science & Business Media. This book was released on 2011-10-21 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: The emphasis throughout the present volume is on the practical application of theoretical mathematical models helping to unravel the underlying mechanisms involved in processes from mathematical physics and biosciences. It has been conceived as a unique collection of abstract methods dealing especially with nonlinear partial differential equations (either stationary or evolutionary) that are applied to understand concrete processes involving some important applications related to phenomena such as: boundary layer phenomena for viscous fluids, population dynamics,, dead core phenomena, etc. It addresses researchers and post-graduate students working at the interplay between mathematics and other fields of science and technology and is a comprehensive introduction to the theory of nonlinear partial differential equations and its main principles also presents their real-life applications in various contexts: mathematical physics, chemistry, mathematical biology, and population genetics. Based on the authors' original work, this volume provides an overview of the field, with examples suitable for researchers but also for graduate students entering research. The method of presentation appeals to readers with diverse backgrounds in partial differential equations and functional analysis. Each chapter includes detailed heuristic arguments, providing thorough motivation for the material developed later in the text. The content demonstrates in a firm way that partial differential equations can be used to address a large variety of phenomena occurring in and influencing our daily lives. The extensive reference list and index make this book a valuable resource for researchers working in a variety of fields and who are interested in phenomena modeled by nonlinear partial differential equations.
Download or read book Partial Differential Equations III written by Michael E. Taylor and published by Springer Nature. This book was released on 2023-12-06 with total page 774 pages. Available in PDF, EPUB and Kindle. Book excerpt: The third of three volumes on partial differential equations, this is devoted to nonlinear PDE. It treats a number of equations of classical continuum mechanics, including relativistic versions, as well as various equations arising in differential geometry, such as in the study of minimal surfaces, isometric imbedding, conformal deformation, harmonic maps, and prescribed Gauss curvature. In addition, some nonlinear diffusion problems are studied. It also introduces such analytical tools as the theory of L^p Sobolev spaces, Holder spaces, Hardy spaces, and Morrey spaces, and also a development of Calderon-Zygmund theory and paradifferential operator calculus. The book is targeted at graduate students in mathematics and at professional mathematicians with an interest in partial differential equations, mathematical physics, differential geometry, harmonic analysis, and complex analysis. The third edition further expands the material by incorporating new theorems and applications throughout the book, and by deepening connections and relating concepts across chapters. It includes new sections on rigid body motion, on probabilistic results related to random walks, on aspects of operator theory related to quantum mechanics, on overdetermined systems, and on the Euler equation for incompressible fluids. The appendices have also been updated with additional results, ranging from weak convergence of measures to the curvature of Kahler manifolds. Michael E. Taylor is a Professor of Mathematics at the University of North Carolina, Chapel Hill, NC. Review of first edition: “These volumes will be read by several generations of readers eager to learn the modern theory of partial differential equations of mathematical physics and the analysis in which this theory is rooted.” (Peter Lax, SIAM review, June 1998)
Download or read book Applications of Nonlinear Partial Differential Equations in Mathematical Physics written by and published by . This book was released on 1965 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Nonlinear Partial Differential Equations in Engineering and Applied Science written by Robert L. Sternberg and published by CRC Press. This book was released on 1980-06-01 with total page 512 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this volume are twenty-eight papers from the Conference on Nonlinear Partial Differential Equationsin Engineering and Applied Science, sponsored by the Office of Naval Research and held at the Universityof Rhode Island in June, 1979. Included are contributions from an international group of distinguishedmathematicians, scientists, and engineers coming from a wide variety of disciplines and having a commoninterest in the application of mathematics, particularly nonlinear partial differential equations, to realworld problems.The subject matter ranges from almost purely mathematical topics in numerical analysis and bifurcationtheory to a host of practical applications that involve nonlinear partial differential equations, suchas fluid dynamics, nonlinear waves, elasticity, viscoelasticity, hyperelasticity, solitons, metallurgy, shocklessairfoil design, quantum fields, and Darcy's law on flows in porous media.Non/inear Partial Differential Equations in Engineering and Applied Science focuses on a variety oftopics of specialized, contemporary concern to mathematicians, physical and biological scientists, andengineers who work with phenomena that can be described by nonlinear partial differential equations.
Download or read book Nonlinear Partial Differential Equations with Applications written by Tomáš Roubíček and published by Springer Science & Business Media. This book was released on 2013-01-13 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition leads the reader through the general theory based on abstract (pseudo-) monotone or accretive operators as fast as possible towards the analysis of concrete differential equations, which have specific applications in continuum (thermo-) mechanics of solids and fluids, electrically (semi-) conductive media, modelling of biological systems, or in mechanical engineering. Selected parts are mainly an introduction into the subject while some others form an advanced textbook. The second edition simplifies and extends the exposition at particular spots and augments the applications especially towards thermally coupled systems, magnetism, and more. The intended audience is graduate and PhD students as well as researchers in the theory of partial differential equations or in mathematical modelling of distributed parameter systems. ------ The monograph contains a wealth of material in both the abstract theory of steady-state or evolution equations of monotone and accretive type and concrete applications to nonlinear partial differential equations from mathematical modeling. The organization of the material is well done, and the presentation, although concise, is clear, elegant and rigorous. (...) this book is a notable addition to the existing literature. Also, it certainly will prove useful to engineers, physicists, biologists and other scientists interested in the analysis of (...) nonlinear differential models of the real world. (Mathematical Reviews)
Download or read book Nonlinear Partial Differential Equations written by Luis A. Caffarelli and published by Springer Science & Business Media. This book was released on 2012-02-02 with total page 156 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book covers several topics of current interest in the field of nonlinear partial differential equations and their applications to the physics of continuous media and particle interactions. It treats the quasigeostrophic equation, integral diffusions, periodic Lorentz gas, Boltzmann equation, and critical dispersive nonlinear Schrödinger and wave equations. The book describes in a careful and expository manner several powerful methods from recent top research articles.