Nonlinear Differential Equation Models

Author : Ansgar Jüngel,Raul Manasevich,Peter A. Markowich,Henrik Shahgholian
Publisher : Springer Science & Business Media
Page : 195 pages
File Size : 48,5 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783709106099

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Nonlinear Differential Equation Models by Ansgar Jüngel,Raul Manasevich,Peter A. Markowich,Henrik Shahgholian Pdf

The papers in this book originate from lectures which were held at the "Vienna Workshop on Nonlinear Models and Analysis" – May 20–24, 2002. They represent a cross-section of the research field Applied Nonlinear Analysis with emphasis on free boundaries, fully nonlinear partial differential equations, variational methods, quasilinear partial differential equations and nonlinear kinetic models.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 52,6 Mb
Release : 2024-06-26
Category : Electronic
ISBN : 9789814468169

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Modeling By Nonlinear Differential Equations by Anonim Pdf

Author : Paul Edgar Phillipson
Publisher : World Scientific
Page : 238 pages
File Size : 40,7 Mb
Release : 2009
Category : Mathematics
ISBN : 9789814271608

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Modeling by Nonlinear Differential Equations by Paul Edgar Phillipson Pdf

This book aims to provide mathematical analyses of nonlinear differential equations, which have proved pivotal to understanding many phenomena in physics, chemistry and biology. Topics of focus are autocatalysis and dynamics of molecular evolution, relaxation oscillations, deterministic chaos, reaction diffusion driven chemical pattern formation, solitons and neuron dynamics. Included is a discussion of processes from the viewpoints of reversibility, reflected by conservative classical mechanics, and irreversibility introduced by the dissipative role of diffusion. Each chapter presents the subject matter from the point of one or a few key equations, whose properties and consequences are amplified by approximate analytic solutions that are developed to support graphical display of exact computer solutions. Sample Chapter(s). Chapter 1: Theme and Contents of this Book (85 KB). Contents: Theme and Contents of this Book; Processes in closed and Open Systems; Dynamics of Molecular Evolution; Relaxation Oscillations; Order and Chaos; Reaction Diffusion Dynamics; Solitons; Neuron Pulse Propagation; Time Reversal, Dissipation and Conservation. Readership: Advanced undergraduates, graduate students and researchers in physics, chemistry, biology or bioinformatics who are interested in mathematical modeling.

Author : Feliz Manuel Minhós,João Fialho
Publisher : MDPI
Page : 158 pages
File Size : 52,9 Mb
Release : 2021-04-15
Category : Mathematics
ISBN : 9783036507101

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Nonlinear Differential Equations and Dynamical Systems by Feliz Manuel Minhós,João Fialho Pdf

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.

Author : Ansgar Jüngel,Raul Manasevich,Peter A. Markowich,Henrik Shahgholian
Publisher : Springer Science & Business Media
Page : 216 pages
File Size : 40,9 Mb
Release : 2004-06-14
Category : Mathematics
ISBN : 3211209956

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Nonlinear Differential Equation Models by Ansgar Jüngel,Raul Manasevich,Peter A. Markowich,Henrik Shahgholian Pdf

The papers in this book originate from lectures which were held at the "Vienna Workshop on Nonlinear Models and Analysis" – May 20–24, 2002. They represent a cross-section of the research field Applied Nonlinear Analysis with emphasis on free boundaries, fully nonlinear partial differential equations, variational methods, quasilinear partial differential equations and nonlinear kinetic models.

Author : James Dickson Murray
Publisher : Oxford University Press, USA
Page : 392 pages
File Size : 52,9 Mb
Release : 1977
Category : Mathematics
ISBN : CORNELL:31924001306608

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Lectures on Nonlinear-differential-equation Models in Biology by James Dickson Murray Pdf

Author : Marius Ghergu,Vicentiu RADULESCU
Publisher : Springer Science & Business Media
Page : 402 pages
File Size : 49,6 Mb
Release : 2011-10-21
Category : Mathematics
ISBN : 9783642226649

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Nonlinear PDEs by Marius Ghergu,Vicentiu RADULESCU Pdf

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.​

Author : John R. Hauser
Publisher : Springer Science & Business Media
Page : 1013 pages
File Size : 52,9 Mb
Release : 2009-03-24
Category : Technology & Engineering
ISBN : 9781402099205

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Numerical Methods for Nonlinear Engineering Models by John R. Hauser Pdf

There are many books on the use of numerical methods for solving engineering problems and for modeling of engineering artifacts. In addition there are many styles of such presentations ranging from books with a major emphasis on theory to books with an emphasis on applications. The purpose of this book is hopefully to present a somewhat different approach to the use of numerical methods for - gineering applications. Engineering models are in general nonlinear models where the response of some appropriate engineering variable depends in a nonlinear manner on the - plication of some independent parameter. It is certainly true that for many types of engineering models it is sufficient to approximate the real physical world by some linear model. However, when engineering environments are pushed to - treme conditions, nonlinear effects are always encountered. It is also such - treme conditions that are of major importance in determining the reliability or failure limits of engineering systems. Hence it is essential than engineers have a toolbox of modeling techniques that can be used to model nonlinear engineering systems. Such a set of basic numerical methods is the topic of this book. For each subject area treated, nonlinear models are incorporated into the discussion from the very beginning and linear models are simply treated as special cases of more general nonlinear models. This is a basic and fundamental difference in this book from most books on numerical methods.

Author : Tomás Roubicek
Publisher : Springer Science & Business Media
Page : 405 pages
File Size : 51,8 Mb
Release : 2006-01-17
Category : Mathematics
ISBN : 9783764373979

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Nonlinear Partial Differential Equations with Applications by Tomás Roubicek Pdf

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.

Author : Daniela Lupo,Carlo Pagani,Bernhard Ruf
Publisher : Springer Science & Business Media
Page : 284 pages
File Size : 47,9 Mb
Release : 2003-09-25
Category : Mathematics
ISBN : 3764303980

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Nonlinear Equations: Methods, Models and Applications by Daniela Lupo,Carlo Pagani,Bernhard Ruf Pdf

A collection of research articles originating from the Workshop on Nonlinear Analysis and Applications held in Bergamo in July 2001. Classical topics of nonlinear analysis were considered, such as calculus of variations, variational inequalities, critical point theory and their use in various aspects of the study of elliptic differential equations and systems, equations of Hamilton-Jacobi, Schrödinger and Navier-Stokes, and free boundary problems. Moreover, various models were focused upon: travelling waves in supported beams and plates, vortex condensation in electroweak theory, information theory, non-geometrical optics, and Dirac-Fock models for heavy atoms.

Author : Piero de Mottoni,Luigi Salvadori
Publisher : Academic Press
Page : 370 pages
File Size : 40,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483262499

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Nonlinear Differential Equations by Piero de Mottoni,Luigi Salvadori Pdf

Nonlinear Differential Equations: Invariance, Stability, and Bifurcation presents the developments in the qualitative theory of nonlinear differential equations. This book discusses the exchange of mathematical ideas in stability and bifurcation theory. Organized into 26 chapters, this book begins with an overview of the initial value problem for a nonlinear wave equation. This text then focuses on the interplay between stability exchange for a stationary solution and the appearance of bifurcating periodic orbits. Other chapters consider the development of methods for ascertaining stability and boundedness and explore the development of bifurcation and stability analysis in nonlinear models of applied sciences. This book discusses as well nonlinear hyperbolic equations in further contributions, featuring stability properties of periodic and almost periodic solutions. The reader is also introduced to the stability problem of the equilibrium of a chemical network. The final chapter deals with suitable spaces for studying functional equations. This book is a valuable resource for mathematicians.

Author : Daniela Lupo,Carlo Pagani,Bernhard Ruf
Publisher : Birkhäuser
Page : 268 pages
File Size : 49,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9783034880879

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Nonlinear Equations: Methods, Models and Applications by Daniela Lupo,Carlo Pagani,Bernhard Ruf Pdf

A collection of research articles originating from the Workshop on Nonlinear Analysis and Applications held in Bergamo in July 2001. Classical topics of nonlinear analysis were considered, such as calculus of variations, variational inequalities, critical point theory and their use in various aspects of the study of elliptic differential equations and systems, equations of Hamilton-Jacobi, Schrödinger and Navier-Stokes, and free boundary problems. Moreover, various models were focused upon: travelling waves in supported beams and plates, vortex condensation in electroweak theory, information theory, non-geometrical optics, and Dirac-Fock models for heavy atoms.

Author : Boris P. Bezruchko,Dmitry A. Smirnov
Publisher : Springer Science & Business Media
Page : 416 pages
File Size : 51,9 Mb
Release : 2010-09-03
Category : Science
ISBN : 9783642126017

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Extracting Knowledge From Time Series by Boris P. Bezruchko,Dmitry A. Smirnov Pdf

Mathematical modelling is ubiquitous. Almost every book in exact science touches on mathematical models of a certain class of phenomena, on more or less speci?c approaches to construction and investigation of models, on their applications, etc. As many textbooks with similar titles, Part I of our book is devoted to general qu- tions of modelling. Part II re?ects our professional interests as physicists who spent much time to investigations in the ?eld of non-linear dynamics and mathematical modelling from discrete sequences of experimental measurements (time series). The latter direction of research is known for a long time as “system identi?cation” in the framework of mathematical statistics and automatic control theory. It has its roots in the problem of approximating experimental data points on a plane with a smooth curve. Currently, researchers aim at the description of complex behaviour (irregular, chaotic, non-stationary and noise-corrupted signals which are typical of real-world objects and phenomena) with relatively simple non-linear differential or difference model equations rather than with cumbersome explicit functions of time. In the second half of the twentieth century, it has become clear that such equations of a s- ?ciently low order can exhibit non-trivial solutions that promise suf?ciently simple modelling of complex processes; according to the concepts of non-linear dynamics, chaotic regimes can be demonstrated already by a third-order non-linear ordinary differential equation, while complex behaviour in a linear model can be induced either by random in?uence (noise) or by a very high order of equations.

Author : Pavel Drabek
Publisher : CRC Press
Page : 212 pages
File Size : 48,6 Mb
Release : 2024-05-17
Category : Mathematics
ISBN : 9781000673494

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Nonlinear Differential Equations by Pavel Drabek Pdf

Working with mathematical models today requires in-depth knowledge of recent methods developed for solving nonlinear differential equations. Keeping abreast of these developments is the goal of the regular meetings of nonlinear analysts held in the Czech Republic, the most recent of which formed the basis of this volume. The subject addressed by these authors is the theory of nonlinear differential equations, with focus on the quasilinear elliptic differential equations of the degenerate type.

Author : Nail H. Ibragimov,Nail? Kha?rullovich Ibragimov
Publisher : World Scientific
Page : 365 pages
File Size : 49,9 Mb
Release : 2009
Category : Mathematics
ISBN : 9789814291958

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A Practical Course in Differential Equations and Mathematical Modelling by Nail H. Ibragimov,Nail? Kha?rullovich Ibragimov Pdf

A Practical Course in Differential Equations and Mathematical Modelling is a unique blend of the traditional methods of ordinary and partial differential equations with Lie group analysis enriched by the author?s own theoretical developments. The book ? which aims to present new mathematical curricula based on symmetry and invariance principles ? is tailored to develop analytic skills and ?working knowledge? in both classical and Lie?s methods for solving linear and nonlinear equations. This approach helps to make courses in differential equations, mathematical modelling, distributions and fundamental solution, etc. easy to follow and interesting for students. The book is based on the author?s extensive teaching experience at Novosibirsk and Moscow universities in Russia, CollŠge de France, Georgia Tech and Stanford University in the United States, universities in South Africa, Cyprus, Turkey, and Blekinge Institute of Technology (BTH) in Sweden. The new curriculum prepares students for solving modern nonlinear problems and will essentially be more appealing to students compared to the traditional way of teaching mathematics.