Travelling Waves In Nonlinear Diffusion Convection Reaction

Author : Brian H. Gilding
Publisher : Birkhäuser
ISBN 13 : 3034879644
Total Pages : 214 pages
Book Rating : 4.44/5 ( download)

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Download or read book Travelling Waves in Nonlinear Diffusion-Convection Reaction written by Brian H. Gilding and published by Birkhäuser. This book was released on 2012-12-06 with total page 214 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph has grown out of research we started in 1987, although the foun dations were laid in the 1970's when both of us were working on our doctoral theses, trying to generalize the now classic paper of Oleinik, Kalashnikov and Chzhou on nonlinear degenerate diffusion. Brian worked under the guidance of Bert Peletier at the University of Sussex in Brighton, England, and, later at Delft University of Technology in the Netherlands on extending the earlier mathematics to include nonlinear convection; while Robert worked at Lomonosov State Univer sity in Moscow under the supervision of Anatolii Kalashnikov on generalizing the earlier mathematics to include nonlinear absorption. We first met at a conference held in Rome in 1985. In 1987 we met again in Madrid at the invitation of Ildefonso Diaz, where we were both staying at 'La Residencia'. As providence would have it, the University 'Complutense' closed down during this visit in response to student demonstra tions, and, we were very much left to our own devices. It was natural that we should gravitate to a research topic of common interest. This turned out to be the characterization of the phenomenon of finite speed of propagation for nonlin ear reaction-convection-diffusion equations. Brian had just completed some work on this topic for nonlinear diffusion-convection, while Robert had earlier done the same for nonlinear diffusion-absorption. There was no question but that we bundle our efforts on the general situation.

Author : B. H. Gilding
Publisher :
ISBN 13 :
Total Pages : 188 pages
Book Rating : 4.37/5 ( download)

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Download or read book Travelling Waves in Nonlinear Diffusion-convection-reation written by B. H. Gilding and published by . This book was released on 2001 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Roman Cherniha
Publisher : CRC Press
ISBN 13 : 1498776191
Total Pages : 261 pages
Book Rating : 4.96/5 ( download)

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Download or read book Nonlinear Reaction-Diffusion-Convection Equations written by Roman Cherniha and published by CRC Press. This book was released on 2017-11-02 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well known that symmetry-based methods are very powerful tools for investigating nonlinear partial differential equations (PDEs), notably for their reduction to those of lower dimensionality (e.g. to ODEs) and constructing exact solutions. This book is devoted to (1) search Lie and conditional (non-classical) symmetries of nonlinear RDC equations, (2) constructing exact solutions using the symmetries obtained, and (3) their applications for solving some biologically and physically motivated problems. The book summarises the results derived by the authors during the last 10 years and those obtained by some other authors.

Author : Graham Griffiths
Publisher : Academic Press
ISBN 13 : 0123846536
Total Pages : 463 pages
Book Rating : 4.32/5 ( download)

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Download or read book Traveling Wave Analysis of Partial Differential Equations written by Graham Griffiths and published by Academic Press. This book was released on 2010-12-09 with total page 463 pages. Available in PDF, EPUB and Kindle. Book excerpt: Although the Partial Differential Equations (PDE) models that are now studied are usually beyond traditional mathematical analysis, the numerical methods that are being developed and used require testing and validation. This is often done with PDEs that have known, exact, analytical solutions. The development of analytical solutions is also an active area of research, with many advances being reported recently, particularly traveling wave solutions for nonlinear evolutionary PDEs. Thus, the current development of analytical solutions directly supports the development of numerical methods by providing a spectrum of test problems that can be used to evaluate numerical methods. This book surveys some of these new developments in analytical and numerical methods, and relates the two through a series of PDE examples. The PDEs that have been selected are largely "named'' since they carry the names of their original contributors. These names usually signify that the PDEs are widely recognized and used in many application areas. The authors’ intention is to provide a set of numerical and analytical methods based on the concept of a traveling wave, with a central feature of conversion of the PDEs to ODEs. The Matlab and Maple software will be available for download from this website shortly. www.pdecomp.net Includes a spectrum of applications in science, engineering, applied mathematics Presents a combination of numerical and analytical methods Provides transportable computer codes in Matlab and Maple

Author : Massimo Cicognani
Publisher : Springer Nature
ISBN 13 : 3030613461
Total Pages : 469 pages
Book Rating : 4.64/5 ( download)

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Download or read book Anomalies in Partial Differential Equations written by Massimo Cicognani and published by Springer Nature. This book was released on 2021-02-03 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: The contributions contained in the volume, written by leading experts in their respective fields, are expanded versions of talks given at the INDAM Workshop "Anomalies in Partial Differential Equations" held in September 2019 at the Istituto Nazionale di Alta Matematica, Dipartimento di Matematica "Guido Castelnuovo", Università di Roma "La Sapienza". The volume contains results for well-posedness and local solvability for linear models with low regular coefficients. Moreover, nonlinear dispersive models (damped waves, p-evolution models) are discussed from the point of view of critical exponents, blow-up phenomena or decay estimates for Sobolev solutions. Some contributions are devoted to models from applications as traffic flows, Einstein-Euler systems or stochastic PDEs as well. Finally, several contributions from Harmonic and Time-Frequency Analysis, in which the authors are interested in the action of localizing operators or the description of wave front sets, complete the volume.

Author : Freddy Dumortier
Publisher : World Scientific
ISBN 13 : 9814480916
Total Pages : 1180 pages
Book Rating : 4.18/5 ( download)

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Download or read book Equadiff 2003 - Proceedings Of The International Conference On Differential Equations written by Freddy Dumortier and published by World Scientific. This book was released on 2005-02-23 with total page 1180 pages. Available in PDF, EPUB and Kindle. Book excerpt: This comprehensive volume contains the state of the art on ODE's and PDE's of different nature, functional differential equations, delay equations, and others, mostly from the dynamical systems point of view.A broad range of topics are treated through contributions by leading experts of their fields, presenting the most recent developments. A large variety of techniques are being used, stressing geometric, topological, ergodic and numerical aspects.The scope of the book is wide, ranging from pure mathematics to various applied fields. Examples of the latter are provided by subjects from earth and life sciences, classical mechanics and quantum-mechanics, among others.The proceedings have been selected for coverage in:• Index to Scientific & Technical Proceedings® (ISTP® / ISI Proceedings)• Index to Scientific & Technical Proceedings (ISTP CDROM version / ISI Proceedings)• CC Proceedings — Engineering & Physical Sciences

Author : Stanislav Antontsev
Publisher : Springer
ISBN 13 : 9462391122
Total Pages : 417 pages
Book Rating : 4.23/5 ( download)

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Download or read book Evolution PDEs with Nonstandard Growth Conditions written by Stanislav Antontsev and published by Springer. This book was released on 2015-04-01 with total page 417 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph offers the reader a treatment of the theory of evolution PDEs with nonstandard growth conditions. This class includes parabolic and hyperbolic equations with variable or anisotropic nonlinear structure. We develop methods for the study of such equations and present a detailed account of recent results. An overview of other approaches to the study of PDEs of this kind is provided. The presentation is focused on the issues of existence and uniqueness of solutions in appropriate function spaces and on the study of the specific qualitative properties of solutions, such as localization in space and time, extinction in a finite time and blow-up, or nonexistence of global in time solutions. Special attention is paid to the study of the properties intrinsic to solutions of equations with nonstandard growth.

Author : Anna R. Ghazaryan
Publisher : CRC Press
ISBN 13 : 100077693X
Total Pages : 160 pages
Book Rating : 4.35/5 ( download)

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Download or read book Introduction to Traveling Waves written by Anna R. Ghazaryan and published by CRC Press. This book was released on 2022-11-14 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduction to Traveling Waves is an invitation to research focused on traveling waves for undergraduate and masters level students. Traveling waves are not typically covered in the undergraduate curriculum, and topics related to traveling waves are usually only covered in research papers, except for a few texts designed for students. This book includes techniques that are not covered in those texts. Through their experience involving undergraduate and graduate students in a research topic related to traveling waves, the authors found that the main difficulty is to provide reading materials that contain the background information sufficient to start a research project without an expectation of an extensive list of prerequisites beyond regular undergraduate coursework. This book meets that need and serves as an entry point into research topics about the existence and stability of traveling waves. Features Self-contained, step-by-step introduction to nonlinear waves written assuming minimal prerequisites, such as an undergraduate course on linear algebra and differential equations. Suitable as a textbook for a special topics course, or as supplementary reading for courses on modeling. Contains numerous examples to support the theoretical material. Supplementary MATLAB codes available via GitHub.

Author : Arianna Bianchi
Publisher : Springer Nature
ISBN 13 : 3030225836
Total Pages : 267 pages
Book Rating : 4.34/5 ( download)

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Download or read book The Dynamics of Biological Systems written by Arianna Bianchi and published by Springer Nature. This book was released on 2019-10-02 with total page 267 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents nine mini-courses from a summer school, Dynamics of Biological Systems, held at the University of Alberta in 2016, as part of the prestigious seminar series: Séminaire de Mathématiques Supérieures (SMS). It includes new and significant contributions in the field of Dynamical Systems and their applications in Biology, Ecology, and Medicine. The chapters of this book cover a wide range of mathematical methods and biological applications. They - explain the process of mathematical modelling of biological systems with many examples, - introduce advanced methods from dynamical systems theory, - present many examples of the use of mathematical modelling to gain biological insight - discuss innovative methods for the analysis of biological processes, - contain extensive lists of references, which allow interested readers to continue the research on their own. Integrating the theory of dynamical systems with biological modelling, the book will appeal to researchers and graduate students in Applied Mathematics and Life Sciences.

Author : Michel Chipot
Publisher : Springer Science & Business Media
ISBN 13 : 9783764372668
Total Pages : 556 pages
Book Rating : 4.64/5 ( download)

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Download or read book Nonlinear Elliptic and Parabolic Problems written by Michel Chipot and published by Springer Science & Business Media. This book was released on 2005-10-18 with total page 556 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present volume is dedicated to celebrate the work of the renowned mathematician Herbert Amann, who had a significant and decisive influence in shaping Nonlinear Analysis. Most articles published in this book, which consists of 32 articles in total, written by highly distinguished researchers, are in one way or another related to the scientific works of Herbert Amann. The contributions cover a wide range of nonlinear elliptic and parabolic equations with applications to natural sciences and engineering. Special topics are fluid dynamics, reaction-diffusion systems, bifurcation theory, maximal regularity, evolution equations, and the theory of function spaces.