Nonlinear Differential Equations And Applications
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Nonlinear Partial Differential Equations With Applications
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Author : Tomás Roubicek
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-01-17
Nonlinear Partial Differential Equations With Applications written by Tomás Roubicek and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-01-17 with Mathematics categories.
This book primarily concerns quasilinear and semilinear elliptic and parabolic partial differential equations, inequalities, and systems. The exposition quickly leads general theory to analysis of concrete equations, which have specific applications in such areas as electrically (semi-) conductive media, modeling of biological systems, and mechanical engineering. Methods of Galerkin or of Rothe are exposed in a large generality.
Nonlinear Partial Differential Equations With Applications
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Author : Tomáš Roubíček
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-01-13
Nonlinear Partial Differential Equations With Applications written by Tomáš Roubíček and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-01-13 with Mathematics categories.
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)
Nonlinear Partial Differential Equations
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Author : Mi-Ho Giga
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-05-30
Nonlinear Partial Differential Equations written by Mi-Ho Giga and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-05-30 with Mathematics categories.
This work will serve as an excellent first course in modern analysis. The main focus is on showing how self-similar solutions are useful in studying the behavior of solutions of nonlinear partial differential equations, especially those of parabolic type. This textbook will be an excellent resource for self-study or classroom use.
Introduction To Nonlinear Differential And Integral Equations
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Author : Harold Thayer Davis
language : en
Publisher: Courier Corporation
Release Date : 1962-01-01
Introduction To Nonlinear Differential And Integral Equations written by Harold Thayer Davis and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962-01-01 with Mathematics categories.
Topics covered include differential equations of the 1st order, the Riccati equation and existence theorems, 2nd order equations, elliptic integrals and functions, nonlinear mechanics, nonlinear integral equations, more. Includes 137 problems.
Existence Theory For Nonlinear Ordinary Differential Equations
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Author : Donal O'Regan
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Existence Theory For Nonlinear Ordinary Differential Equations written by Donal O'Regan and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
We begin our applications of fixed point methods with existence of solutions to certain first order initial initial value problems. This problem is relatively easy to treat, illustrates important methods, and in the end will carry us a good deal further than may first meet the eye. Thus, we seek solutions to Y'. = I(t,y) (1. 1 ) { yeO) = r n where I: I X R n ---+ R and I = [0, b]. We shall seek solutions that are de fined either locally or globally on I, according to the assumptions imposed on I. Notice that (1. 1) is a system of first order equations because I takes its values in Rn. In section 3. 2 we will first establish some basic existence theorems which guarantee that a solution to (1. 1) exists for t > 0 and near zero. Familiar examples show that the interval of existence can be arbi trarily short, depending on the initial value r and the nonlinear behaviour of I. As a result we will also examine in section 3. 2 the dependence of the interval of existence on I and r. We mention in passing that, in the results which follow, the interval I can be replaced by any bounded interval and the initial value can be specified at any point in I. The reasoning needed to cover this slightly more general situation requires minor modifications on the arguments given here.
Nonlinear Differential Equations And Dynamical Systems
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Author : Feliz Manuel Minhós
language : en
Publisher: MDPI
Release Date : 2021-04-15
Nonlinear Differential Equations And Dynamical Systems 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 2021-04-15 with Mathematics categories.
This Special Edition contains new results on Differential and Integral Equations and Systems, covering higher-order Initial and Boundary Value Problems, fractional differential and integral equations and applications, non-local optimal control, inverse, and higher-order nonlinear boundary value problems, distributional solutions in the form of a finite series of the Dirac delta function and its derivatives, asymptotic properties’ oscillatory theory for neutral nonlinear differential equations, the existence of extremal solutions via monotone iterative techniques, predator–prey interaction via fractional-order models, among others. Our main goal is not only to show new trends in this field but also to showcase and provide new methods and techniques that can lead to future research.
Nonlinear Systems Of Partial Differential Equations Applications To Life And Physical Sciences
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Author : Anthony W Leung
language : en
Publisher: World Scientific
Release Date : 2009-08-28
Nonlinear Systems Of Partial Differential Equations Applications To Life And Physical Sciences written by Anthony W Leung and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-08-28 with Mathematics categories.
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.
The Pullback Equation For Differential Forms
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Author : Gyula Csató
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-12
The Pullback Equation For Differential Forms written by Gyula Csató and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-12 with Mathematics categories.
An important question in geometry and analysis is to know when two k-forms f and g are equivalent through a change of variables. The problem is therefore to find a map φ so that it satisfies the pullback equation: φ*(g) = f. In more physical terms, the question under consideration can be seen as a problem of mass transportation. The problem has received considerable attention in the cases k = 2 and k = n, but much less when 3 ≤ k ≤ n–1. The present monograph provides the first comprehensive study of the equation. The work begins by recounting various properties of exterior forms and differential forms that prove useful throughout the book. From there it goes on to present the classical Hodge–Morrey decomposition and to give several versions of the Poincaré lemma. The core of the book discusses the case k = n, and then the case 1≤ k ≤ n–1 with special attention on the case k = 2, which is fundamental in symplectic geometry. Special emphasis is given to optimal regularity, global results and boundary data. The last part of the work discusses Hölder spaces in detail; all the results presented here are essentially classical, but cannot be found in a single book. This section may serve as a reference on Hölder spaces and therefore will be useful to mathematicians well beyond those who are only interested in the pullback equation. The Pullback Equation for Differential Forms is a self-contained and concise monograph intended for both geometers and analysts. The book may serve as a valuable reference for researchers or a supplemental text for graduate courses or seminars.
Applications Of Nonlinear Analysis
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Author : Themistocles M. Rassias
language : en
Publisher: Springer
Release Date : 2018-06-29
Applications Of Nonlinear Analysis written by Themistocles M. Rassias and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-29 with Mathematics categories.
New applications, research, and fundamental theories in nonlinear analysis are presented in this book. Each chapter provides a unique insight into a large domain of research focusing on functional equations, stability theory, approximation theory, inequalities, nonlinear functional analysis, and calculus of variations with applications to optimization theory. Topics include: Fixed point theory Fixed-circle theory Coupled fixed points Nonlinear duality in Banach spaces Jensen's integral inequality and applications Nonlinear differential equations Nonlinear integro-differential equations Quasiconvexity, Stability of a Cauchy-Jensen additive mapping Generalizations of metric spaces Hilbert-type integral inequality, Solitons Quadratic functional equations in fuzzy Banach spaces Asymptotic orbits in Hill’sproblem Time-domain electromagnetics Inertial Mann algorithms Mathematical modelling Robotics Graduate students and researchers will find this book helpful in comprehending current applications and developments in mathematical analysis. Research scientists and engineers studying essential modern methods and techniques to solve a variety of problems will find this book a valuable source filled with examples that illustrate concepts.
Ordinary Differential Equations With Applications
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Author : Carmen Chicone
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-04-08
Ordinary Differential Equations With Applications written by Carmen Chicone and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-04-08 with Mathematics categories.
This book is based on a two-semester course in ordinary di?erential eq- tions that I have taught to graduate students for two decades at the U- versity of Missouri. The scope of the narrative evolved over time from an embryonic collection of supplementary notes, through many classroom tested revisions, to a treatment of the subject that is suitable for a year (or more) of graduate study. If it is true that students of di?erential equations giveaway their point of viewbythewaytheydenotethederivativewith respecttotheindependent variable, then the initiated reader can turn to Chapter 1, note that I write x ?,not x , and thus correctly deduce that this book is written with an eye toward dynamical systems. Indeed, this book contains a thorough int- duction to the basic properties of di?erential equations that are needed to approach the modern theory of (nonlinear) dynamical systems. However, this is not the whole story. The book is also a product of my desire to demonstrate to my students that di?erential equations is the least insular of mathematical subjects, that it is strongly connected to almost all areas of mathematics, and it is an essential element of applied mathematics.