Nonlinear Systems Of Partial Differential Equations In Applied Mathematics

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Nonlinear Systems of Partial Differential Equations in Applied Mathematics

Author : Basil Nicolaenko
Publisher : American Mathematical Soc.
ISBN 13 : 9780821896891
Total Pages : 490 pages
Book Rating : 4.8/5 (968 download)

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Book Synopsis Nonlinear Systems of Partial Differential Equations in Applied Mathematics by : Basil Nicolaenko

Download or read book Nonlinear Systems of Partial Differential Equations in Applied Mathematics written by Basil Nicolaenko and published by American Mathematical Soc.. This book was released on 1986-12-31 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: These two volumes of 47 papers focus on the increased interplay of theoretical advances in nonlinear hyperbolic systems, completely integrable systems, and evolutionary systems of nonlinear partial differential equations. The papers both survey recent results and indicate future research trends in these vital and rapidly developing branches of PDEs. The editor has grouped the papers loosely into the following five sections: integrable systems, hyperbolic systems, variational problems, evolutionary systems, and dispersive systems. However, the variety of the subjects discussed as well as their many interwoven trends demonstrate that it is through interactive advances that such rapid progress has occurred. These papers require a good background in partial differential equations. Many of the contributors are mathematical physicists, and the papers are addressed to mathematical physicists (particularly in perturbed integrable systems), as well as to PDE specialists and applied mathematicians in general.

Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1

Author : Basil Nicolaenko
Publisher : American Mathematical Soc.
ISBN 13 : 9780821811252
Total Pages : 494 pages
Book Rating : 4.8/5 (112 download)

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Book Synopsis Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1 by : Basil Nicolaenko

Download or read book Nonlinear Systems of Partial Differential Equations in Applied Mathematics, Part 1 written by Basil Nicolaenko and published by American Mathematical Soc.. This book was released on 1986 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on the increased interplay of theoretical advances in nonlinear hyperbolic systems, completely integrable systems, and evolutionary systems of nonlinear partial differential equations, this title contains papers grouped in sections: integrable systems, hyperbolic systems, variational problems, evolutionary systems, and dispersive systems.

Nonlinear Systems of Partial Differential Equations

Author :
Publisher :
ISBN 13 : 9814467472
Total Pages : pages
Book Rating : 4.8/5 (144 download)

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Book Synopsis Nonlinear Systems of Partial Differential Equations by :

Download or read book Nonlinear Systems of Partial Differential Equations written by and published by . This book was released on with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

An Introduction to Nonlinear Partial Differential Equations

Author : J. David Logan
Publisher : John Wiley & Sons
ISBN 13 : 0470225955
Total Pages : 416 pages
Book Rating : 4.4/5 (72 download)

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Book Synopsis An Introduction to Nonlinear Partial Differential Equations by : J. David Logan

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.

Nonlinear Partial Differential Equations and Their Applications

Author : Doina Cioranescu
Publisher : Elsevier
ISBN 13 : 9780080537672
Total Pages : 664 pages
Book Rating : 4.5/5 (376 download)

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Book Synopsis Nonlinear Partial Differential Equations and Their Applications by : Doina Cioranescu

Download or read book Nonlinear Partial Differential Equations and Their Applications written by Doina Cioranescu and published by Elsevier. This book was released on 2002-06-21 with total page 664 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the written versions of lectures delivered since 1997 in the well-known weekly seminar on Applied Mathematics at the Collège de France in Paris, directed by Jacques-Louis Lions. It is the 14th and last of the series, due to the recent and untimely death of Professor Lions. The texts in this volume deal mostly with various aspects of the theory of nonlinear partial differential equations. They present both theoretical and applied results in many fields of growing importance such as Calculus of variations and optimal control, optimization, system theory and control, operations research, fluids and continuum mechanics, nonlinear dynamics, meteorology and climate, homogenization and material science, numerical analysis and scientific computations The book is of interest to everyone from postgraduate, who wishes to follow the most recent progress in these fields.

Nonlinear Partial Differential Equations in Engineering and Applied Science

Author : Robert L. Sternberg
Publisher : CRC Press
ISBN 13 : 9780824769963
Total Pages : 512 pages
Book Rating : 4.7/5 (699 download)

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Book Synopsis Nonlinear Partial Differential Equations in Engineering and Applied Science by : Robert L. Sternberg

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.

Physical Mathematics and Nonlinear Partial Differential Equations

Author : Lightbourne
Publisher : CRC Press
ISBN 13 : 1000111148
Total Pages : 281 pages
Book Rating : 4.0/5 (1 download)

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Book Synopsis Physical Mathematics and Nonlinear Partial Differential Equations by : Lightbourne

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.

Nonlinear Partial Differential Equations with Applications

Author : Tomás Roubicek
Publisher : Springer Science & Business Media
ISBN 13 : 3764373970
Total Pages : 405 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Nonlinear Partial Differential Equations with Applications by : Tomás Roubicek

Download or read book Nonlinear Partial Differential Equations with Applications written by Tomás Roubicek and published by Springer Science & Business Media. This book was released on 2006-01-17 with total page 405 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 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 for Scientists and Engineers

Author : Lokenath Debnath
Publisher : Springer Science & Business Media
ISBN 13 : 0817682651
Total Pages : 872 pages
Book Rating : 4.8/5 (176 download)

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Book Synopsis Nonlinear Partial Differential Equations for Scientists and Engineers by : Lokenath Debnath

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.

Methods for Constructing Exact Solutions of Partial Differential Equations

Author : Sergey V. Meleshko
Publisher : Springer Science & Business Media
ISBN 13 : 0387252657
Total Pages : 367 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Methods for Constructing Exact Solutions of Partial Differential Equations by : Sergey V. Meleshko

Download or read book Methods for Constructing Exact Solutions of Partial Differential Equations written by Sergey V. Meleshko and published by Springer Science & Business Media. This book was released on 2006-06-18 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: Differential equations, especially nonlinear, present the most effective way for describing complex physical processes. Methods for constructing exact solutions of differential equations play an important role in applied mathematics and mechanics. This book aims to provide scientists, engineers and students with an easy-to-follow, but comprehensive, description of the methods for constructing exact solutions of differential equations.

Nonlinear Differential Equations

Author : Svatopluk Fucik
Publisher : Elsevier
ISBN 13 : 1483278379
Total Pages : 360 pages
Book Rating : 4.4/5 (832 download)

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Book Synopsis Nonlinear Differential Equations by : Svatopluk Fucik

Download or read book Nonlinear Differential Equations written by Svatopluk Fucik and published by Elsevier. This book was released on 2014-12-03 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Studies in Applied Mathematics, 2: Nonlinear Differential Equations focuses on modern methods of solutions to boundary value problems in linear partial differential equations. The book first tackles linear and nonlinear equations, free boundary problem, second order equations, higher order equations, boundary conditions, and spaces of continuous functions. The text then examines the weak solution of a boundary value problem and variational and topological methods. Discussions focus on general boundary conditions for second order ordinary differential equations, minimal surfaces, existence theorems, potentials of boundary value problems, second derivative of a functional, convex functionals, Lagrange conditions, differential operators, Sobolev spaces, and boundary value problems. The manuscript examines noncoercive problems and vibrational inequalities. Topics include existence theorems, formulation of the problem, vanishing nonlinearities, jumping nonlinearities with finite jumps, rapid nonlinearities, and periodic problems. The text is highly recommended for mathematicians and engineers interested in nonlinear differential equations.

Nonlinear Semigroups, Partial Differential Equations and Attractors

Author : T.L. Gill
Publisher : Springer
ISBN 13 : 3540477918
Total Pages : 194 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Nonlinear Semigroups, Partial Differential Equations and Attractors by : T.L. Gill

Download or read book Nonlinear Semigroups, Partial Differential Equations and Attractors written by T.L. Gill and published by Springer. This book was released on 2006-11-15 with total page 194 pages. Available in PDF, EPUB and Kindle. Book excerpt: The original idea of the organizers of the Washington Symposium was to span a fairly narrow range of topics on some recent techniques developed for the investigation of nonlinear partial differential equations and discuss these in a forum of experts. It soon became clear, however, that the dynamical systems approach interfaced significantly with many important branches of applied mathematics. As a consequence, the scope of this resulting proceedings volume is an enlarged one with coverage of a wider range of research topics.

Separation of Variables and Exact Solutions to Nonlinear PDEs

Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 1000463664
Total Pages : 349 pages
Book Rating : 4.0/5 (4 download)

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Book Synopsis Separation of Variables and Exact Solutions to Nonlinear PDEs by : Andrei D. Polyanin

Download or read book Separation of Variables and Exact Solutions to Nonlinear PDEs written by Andrei D. Polyanin and published by CRC Press. This book was released on 2021-09-20 with total page 349 pages. Available in PDF, EPUB and Kindle. Book excerpt: Separation of Variables and Exact Solutions to Nonlinear PDEs is devoted to describing and applying methods of generalized and functional separation of variables used to find exact solutions of nonlinear partial differential equations (PDEs). It also presents the direct method of symmetry reductions and its more general version. In addition, the authors describe the differential constraint method, which generalizes many other exact methods. The presentation involves numerous examples of utilizing the methods to find exact solutions to specific nonlinear equations of mathematical physics. The equations of heat and mass transfer, wave theory, hydrodynamics, nonlinear optics, combustion theory, chemical technology, biology, and other disciplines are studied. Particular attention is paid to nonlinear equations of a reasonably general form that depend on one or several arbitrary functions. Such equations are the most difficult to analyze. Their exact solutions are of significant practical interest, as they are suitable to assess the accuracy of various approximate analytical and numerical methods. The book contains new material previously unpublished in monographs. It is intended for a broad audience of scientists, engineers, instructors, and students specializing in applied and computational mathematics, theoretical physics, mechanics, control theory, chemical engineering science, and other disciplines. Individual sections of the book and examples are suitable for lecture courses on partial differential equations, equations of mathematical physics, and methods of mathematical physics, for delivering special courses and for practical training.

PETSc for Partial Differential Equations: Numerical Solutions in C and Python

Author : Ed Bueler
Publisher : SIAM
ISBN 13 : 1611976316
Total Pages : 407 pages
Book Rating : 4.6/5 (119 download)

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Book Synopsis PETSc for Partial Differential Equations: Numerical Solutions in C and Python by : Ed Bueler

Download or read book PETSc for Partial Differential Equations: Numerical Solutions in C and Python written by Ed Bueler and published by SIAM. This book was released on 2020-10-22 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Portable, Extensible Toolkit for Scientific Computation (PETSc) is an open-source library of advanced data structures and methods for solving linear and nonlinear equations and for managing discretizations. This book uses these modern numerical tools to demonstrate how to solve nonlinear partial differential equations (PDEs) in parallel. It starts from key mathematical concepts, such as Krylov space methods, preconditioning, multigrid, and Newton’s method. In PETSc these components are composed at run time into fast solvers. Discretizations are introduced from the beginning, with an emphasis on finite difference and finite element methodologies. The example C programs of the first 12 chapters, listed on the inside front cover, solve (mostly) elliptic and parabolic PDE problems. Discretization leads to large, sparse, and generally nonlinear systems of algebraic equations. For such problems, mathematical solver concepts are explained and illustrated through the examples, with sufficient context to speed further development. PETSc for Partial Differential Equations addresses both discretizations and fast solvers for PDEs, emphasizing practice more than theory. Well-structured examples lead to run-time choices that result in high solver performance and parallel scalability. The last two chapters build on the reader’s understanding of fast solver concepts when applying the Firedrake Python finite element solver library. This textbook, the first to cover PETSc programming for nonlinear PDEs, provides an on-ramp for graduate students and researchers to a major area of high-performance computing for science and engineering. It is suitable as a supplement for courses in scientific computing or numerical methods for differential equations.

Computational Solution of Nonlinear Systems of Equations

Author : Eugene L. Allgower
Publisher : American Mathematical Soc.
ISBN 13 : 9780821896945
Total Pages : 788 pages
Book Rating : 4.8/5 (969 download)

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Book Synopsis Computational Solution of Nonlinear Systems of Equations by : Eugene L. Allgower

Download or read book Computational Solution of Nonlinear Systems of Equations written by Eugene L. Allgower and published by American Mathematical Soc.. This book was released on 1990-04-03 with total page 788 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear equations arise in essentially every branch of modern science, engineering, and mathematics. However, in only a very few special cases is it possible to obtain useful solutions to nonlinear equations via analytical calculations. As a result, many scientists resort to computational methods. This book contains the proceedings of the Joint AMS-SIAM Summer Seminar, ``Computational Solution of Nonlinear Systems of Equations,'' held in July 1988 at Colorado State University. The aim of the book is to give a wide-ranging survey of essentially all of the methods which comprise currently active areas of research in the computational solution of systems of nonlinear equations. A number of ``entry-level'' survey papers were solicited, and a series of test problems has been collected in an appendix. Most of the articles are accessible to students who have had a course in numerical analysis.

Nonlinear Ordinary Differential Equations

Author : R. Grimshaw
Publisher : Routledge
ISBN 13 : 1351428098
Total Pages : 336 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Nonlinear Ordinary Differential Equations by : R. Grimshaw

Download or read book Nonlinear Ordinary Differential Equations written by R. Grimshaw and published by Routledge. This book was released on 2017-10-19 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordinary differential equations have long been an important area of study because of their wide application in physics, engineering, biology, chemistry, ecology, and economics. Based on a series of lectures given at the Universities of Melbourne and New South Wales in Australia, Nonlinear Ordinary Differential Equations takes the reader from basic elementary notions to the point where the exciting and fascinating developments in the theory of nonlinear differential equations can be understood and appreciated. Each chapter is self-contained, and includes a selection of problems together with some detailed workings within the main text. Nonlinear Ordinary Differential Equations helps develop an understanding of the subtle and sometimes unexpected properties of nonlinear systems and simultaneously introduces practical analytical techniques to analyze nonlinear phenomena. This excellent book gives a structured, systematic, and rigorous development of the basic theory from elementary concepts to a point where readers can utilize ideas in nonlinear differential equations.

Nonlinear Ordinary Differential Equations

Author : R. Grimshaw
Publisher : Routledge
ISBN 13 : 135142808X
Total Pages : 276 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Nonlinear Ordinary Differential Equations by : R. Grimshaw

Download or read book Nonlinear Ordinary Differential Equations written by R. Grimshaw and published by Routledge. This book was released on 2017-10-19 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ordinary differential equations have long been an important area of study because of their wide application in physics, engineering, biology, chemistry, ecology, and economics. Based on a series of lectures given at the Universities of Melbourne and New South Wales in Australia, Nonlinear Ordinary Differential Equations takes the reader from basic elementary notions to the point where the exciting and fascinating developments in the theory of nonlinear differential equations can be understood and appreciated. Each chapter is self-contained, and includes a selection of problems together with some detailed workings within the main text. Nonlinear Ordinary Differential Equations helps develop an understanding of the subtle and sometimes unexpected properties of nonlinear systems and simultaneously introduces practical analytical techniques to analyze nonlinear phenomena. This excellent book gives a structured, systematic, and rigorous development of the basic theory from elementary concepts to a point where readers can utilize ideas in nonlinear differential equations.