The Fractional Laplacian

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Publisher : World Scientific
ISBN 13 : 9813224010
Total Pages : 342 pages
Book Rating : 4.8/5 (132 download)

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Book Synopsis The Fractional Laplacian by : Wenxiong Chen

Download or read book The Fractional Laplacian written by Wenxiong Chen and published by World Scientific. This book was released on 2020-06-09 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a unique book that provides a comprehensive understanding of nonlinear equations involving the fractional Laplacian as well as other nonlocal operators. Beginning from the definition of fractional Laplacian, it gradually leads the readers to the frontier of current research in this area. The explanations and illustrations are elementary enough so that first year graduate students can follow easily, while it is advanced enough to include many new ideas, methods, and results that appeared recently in research literature, which researchers would find helpful. It focuses on introducing direct methods on the nonlocal problems without going through extensions, such as the direct methods of moving planes, direct method of moving spheres, direct blowing up and rescaling arguments, and so on. Different from most other books, it emphasizes on illuminating the ideas behind the formal concepts and proofs, so that readers can quickly grasp the essence.

Morse Index of Solutions of Nonlinear Elliptic Equations

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Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110537435
Total Pages : 346 pages
Book Rating : 4.1/5 (15 download)

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Book Synopsis Morse Index of Solutions of Nonlinear Elliptic Equations by : Lucio Damascelli

Download or read book Morse Index of Solutions of Nonlinear Elliptic Equations written by Lucio Damascelli and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-07-08 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents in a unified manner the use of the Morse index, and especially its connections to the maximum principle, in the study of nonlinear elliptic equations. The knowledge or a bound on the Morse index of a solution is a very important qualitative information which can be used in several ways for different problems, in order to derive uniqueness, existence or nonexistence, symmetry, and other properties of solutions.

Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations

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Publisher : Hindawi Publishing Corporation
ISBN 13 : 9774540395
Total Pages : 205 pages
Book Rating : 4.7/5 (745 download)

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Book Synopsis Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations by : Vicentiu D. Radulescu

Download or read book Qualitative Analysis of Nonlinear Elliptic Partial Differential Equations written by Vicentiu D. Radulescu and published by Hindawi Publishing Corporation. This book was released on 2008 with total page 205 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a comprehensive introduction to the mathematical theory of nonlinear problems described by elliptic partial differential equations. These equations can be seen as nonlinear versions of the classical Laplace equation, and they appear as mathematical models in different branches of physics, chemistry, biology, genetics, and engineering and are also relevant in differential geometry and relativistic physics. Much of the modern theory of such equations is based on the calculus of variations and functional analysis. Concentrating on single-valued or multivalued elliptic equations with nonlinearities of various types, the aim of this volume is to obtain sharp existence or nonexistence results, as well as decay rates for general classes of solutions. Many technically relevant questions are presented and analyzed in detail. A systematic picture of the most relevant phenomena is obtained for the equations under study, including bifurcation, stability, asymptotic analysis, and optimal regularity of solutions. The method of presentation should appeal to readers with different backgrounds in functional analysis and nonlinear partial differential equations. All chapters include detailed heuristic arguments providing thorough motivation of the study developed later on in the text, in relationship with concrete processes arising in applied sciences. A systematic description of the most relevant singular phenomena described in this volume includes existence (or nonexistence) of solutions, unicity or multiplicity properties, bifurcation and asymptotic analysis, and optimal regularity. The book includes an extensive bibliography and a rich index, thus allowing for quick orientation among the vast collection of literature on the mathematical theory of nonlinear phenomena described by elliptic partial differential equations.

Nonlinear Diffusion Equations and Their Equilibrium States, 3

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Publisher : Springer Science & Business Media
ISBN 13 : 1461203937
Total Pages : 567 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Nonlinear Diffusion Equations and Their Equilibrium States, 3 by : N.G Lloyd

Download or read book Nonlinear Diffusion Equations and Their Equilibrium States, 3 written by N.G Lloyd and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 567 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear diffusion equations have held a prominent place in the theory of partial differential equations, both for the challenging and deep math ematical questions posed by such equations and the important role they play in many areas of science and technology. Examples of current inter est are biological and chemical pattern formation, semiconductor design, environmental problems such as solute transport in groundwater flow, phase transitions and combustion theory. Central to the theory is the equation Ut = ~cp(U) + f(u). Here ~ denotes the n-dimensional Laplacian, cp and f are given functions and the solution is defined on some domain n x [0, T] in space-time. FUn damental questions concern the existence, uniqueness and regularity of so lutions, the existence of interfaces or free boundaries, the question as to whether or not the solution can be continued for all time, the asymptotic behavior, both in time and space, and the development of singularities, for instance when the solution ceases to exist after finite time, either through extinction or through blow up.

Nonlinear Parabolic and Elliptic Equations

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Publisher : Springer Science & Business Media
ISBN 13 : 1461530342
Total Pages : 786 pages
Book Rating : 4.4/5 (615 download)

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Book Synopsis Nonlinear Parabolic and Elliptic Equations by : C.V. Pao

Download or read book Nonlinear Parabolic and Elliptic Equations written by C.V. Pao and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: In response to the growing use of reaction diffusion problems in many fields, this monograph gives a systematic treatment of a class of nonlinear parabolic and elliptic differential equations and their applications these problems. It is an important reference for mathematicians and engineers, as well as a practical text for graduate students.

An Introduction to Maximum Principles and Symmetry in Elliptic Problems

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Publisher : Cambridge University Press
ISBN 13 : 0521461952
Total Pages : 352 pages
Book Rating : 4.5/5 (214 download)

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Book Synopsis An Introduction to Maximum Principles and Symmetry in Elliptic Problems by : L. E. Fraenkel

Download or read book An Introduction to Maximum Principles and Symmetry in Elliptic Problems written by L. E. Fraenkel and published by Cambridge University Press. This book was released on 2000-02-25 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced text, originally published in 2000, on differential equations, with plentiful supply of exercises all with detailed hints.

Contributions to Nonlinear Elliptic Equations and Systems

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Publisher : Birkhäuser
ISBN 13 : 3319199021
Total Pages : 434 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Contributions to Nonlinear Elliptic Equations and Systems by : Alexandre N. Carvalho

Download or read book Contributions to Nonlinear Elliptic Equations and Systems written by Alexandre N. Carvalho and published by Birkhäuser. This book was released on 2015-11-14 with total page 434 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume of contributions pays tribute to the life and work of Djairo Guedes de Figueiredo on the occasion of his 80th birthday. The articles it contains were born out of the ICMC Summer Meeting on Differential Equations – 2014 Chapter, also dedicated to de Figueiredo and held at the Universidade de São Paulo at São Carlos, Brazil from February 3-7, 2014. The contributing authors represent a group of international experts in the field and discuss recent trends and new directions in nonlinear elliptic partial differential equations and systems. Djairo Guedes de Figueiredo has had a very active scientific career, publishing 29 monographs and over one hundred research articles. His influence on Brazilian mathematics has made him one of the pillars of the subject in that country. He had a major impact on the development of analysis, especially in its application to nonlinear elliptic partial differential equations and systems throughout the entire world. The articles collected here pay tribute to him and his legacy and are intended for graduate students and researchers in mathematics and related areas who are interested in nonlinear elliptic partial differential equations and systems.

Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities

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Publisher : Springer Science & Business Media
ISBN 13 : 1461333385
Total Pages : 488 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities by : Zi Cai Li

Download or read book Combined Methods for Elliptic Equations with Singularities, Interfaces and Infinities written by Zi Cai Li and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this book the author sets out to answer two important questions: 1. Which numerical methods may be combined together? 2. How can different numerical methods be matched together? In doing so the author presents a number of useful combinations, for instance, the combination of various FEMs, the combinations of FEM-FDM, REM-FEM, RGM-FDM, etc. The combined methods have many advantages over single methods: high accuracy of solutions, less CPU time, less computer storage, easy coupling with singularities as well as the complicated boundary conditions. Since coupling techniques are essential to combinations, various matching strategies among different methods are carefully discussed. The author provides the matching rules so that optimal convergence, even superconvergence, and optimal stability can be achieved, and also warns of the matching pitfalls to avoid. Audience: The book is intended for both mathematicians and engineers and may be used as text for advanced students.

The Maximum Principle

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Publisher : Springer Science & Business Media
ISBN 13 : 3764381450
Total Pages : 240 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis The Maximum Principle by : Patrizia Pucci

Download or read book The Maximum Principle written by Patrizia Pucci and published by Springer Science & Business Media. This book was released on 2007-12-23 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Maximum principles are bedrock results in the theory of second order elliptic equations. This principle, simple enough in essence, lends itself to a quite remarkable number of subtle uses when combined appropriately with other notions. Intended for a wide audience, the book provides a clear and comprehensive explanation of the various maximum principles available in elliptic theory, from their beginning for linear equations to recent work on nonlinear and singular equations.

Numerical Analysis of Wavelet Methods

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Publisher : Elsevier
ISBN 13 : 0080537855
Total Pages : 357 pages
Book Rating : 4.0/5 (85 download)

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Book Synopsis Numerical Analysis of Wavelet Methods by : A. Cohen

Download or read book Numerical Analysis of Wavelet Methods written by A. Cohen and published by Elsevier. This book was released on 2003-04-29 with total page 357 pages. Available in PDF, EPUB and Kindle. Book excerpt: Since their introduction in the 1980's, wavelets have become a powerful tool in mathematical analysis, with applications such as image compression, statistical estimation and numerical simulation of partial differential equations. One of their main attractive features is the ability to accurately represent fairly general functions with a small number of adaptively chosen wavelet coefficients, as well as to characterize the smoothness of such functions from the numerical behaviour of these coefficients. The theoretical pillar that underlies such properties involves approximation theory and function spaces, and plays a pivotal role in the analysis of wavelet-based numerical methods. This book offers a self-contained treatment of wavelets, which includes this theoretical pillar and it applications to the numerical treatment of partial differential equations. Its key features are:1. Self-contained introduction to wavelet bases and related numerical algorithms, from the simplest examples to the most numerically useful general constructions.2. Full treatment of the theoretical foundations that are crucial for the analysisof wavelets and other related multiscale methods : function spaces, linear and nonlinear approximation, interpolation theory.3. Applications of these concepts to the numerical treatment of partial differential equations : multilevel preconditioning, sparse approximations of differential and integral operators, adaptive discretization strategies.

Handbook of Differential Equations:Stationary Partial Differential Equations

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Publisher : Elsevier
ISBN 13 : 0080461077
Total Pages : 625 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Handbook of Differential Equations:Stationary Partial Differential Equations by : Michel Chipot

Download or read book Handbook of Differential Equations:Stationary Partial Differential Equations written by Michel Chipot and published by Elsevier. This book was released on 2005-08-19 with total page 625 pages. Available in PDF, EPUB and Kindle. Book excerpt: A collection of self contained, state-of-the-art surveys. The authors have made an effort to achieve readability for mathematicians and scientists from other fields, for this series of handbooks to be a new reference for research, learning and teaching.Partial differential equations represent one of the most rapidly developing topics in mathematics. This is due to their numerous applications in science and engineering on the one hand and to the challenge and beauty of associated mathematical problems on the other.Key features:- Self-contained volume in series covering one of the most rapid developing topics in mathematics.- 7 Chapters, enriched with numerous figures originating from numerical simulations.- Written by well known experts in the field.- Self-contained volume in series covering one of the most rapid developing topics in mathematics.- 7 Chapters, enriched with numerous figures originating from numerical simulations.- Written by well known experts in the field.

Progress in Partial Differential Equations

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Publisher :
ISBN 13 :
Total Pages : 220 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Progress in Partial Differential Equations by : Michel Chipot

Download or read book Progress in Partial Differential Equations written by Michel Chipot and published by . This book was released on 1991 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: This Research Note presents some recent advances in three important domains of partial differential equations and applied mathematics: calculus of variations, exact controllability and numerical analysis. These topics are now part of various areas of science and have experienced tremendous development during the last decades. Interconnections within these different areas are also presented in particular for the numerical analysis of problems in calculus of variations and applications to mechanics. Readership: a special attempt has been made to make the results and techniques presented here accessible to young researchers and non-specialists. This book should interest not only experts in partial differential equations but also graduate students, applied mathematicians and computer users.

Variational Methods

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Publisher : Springer Science & Business Media
ISBN 13 : 1475710801
Total Pages : 468 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Variational Methods by : BERESTYCKI

Download or read book Variational Methods written by BERESTYCKI and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the framework of the "Annee non lineaire" (the special nonlinear year) sponsored by the C.N.R.S. (the French National Center for Scien tific Research), a meeting was held in Paris in June 1988. It took place in the Conference Hall of the Ministere de la Recherche and had as an organizing theme the topic of "Variational Problems." Nonlinear analysis has been one of the leading themes in mathemat ical research for the past decade. The use of direct variational methods has been particularly successful in understanding problems arising from physics and geometry. The growth of nonlinear analysis is largely due to the wealth of ap plications from various domains of sciences and industrial applica tions. Most of the papers gathered in this volume have their origin in applications: from mechanics, the study of Hamiltonian systems, from physics, from the recent mathematical theory of liquid crystals, from geometry, relativity, etc. Clearly, no single volume could pretend to cover the whole scope of nonlinear variational problems. We have chosen to concentrate on three main aspects of these problems, organizing them roughly around the following topics: 1. Variational methods in partial differential equations in mathemat ical physics 2. Variational problems in geometry 3. Hamiltonian systems and related topics.

Differential and Integral Equations

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Publisher :
ISBN 13 :
Total Pages : 496 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Differential and Integral Equations by :

Download or read book Differential and Integral Equations written by and published by . This book was released on 2004 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Handbook of Differential Equations: Stationary Partial Differential Equations

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Publisher : Elsevier
ISBN 13 : 0080495060
Total Pages : 736 pages
Book Rating : 4.0/5 (84 download)

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Book Synopsis Handbook of Differential Equations: Stationary Partial Differential Equations by : Michel Chipot

Download or read book Handbook of Differential Equations: Stationary Partial Differential Equations written by Michel Chipot and published by Elsevier. This book was released on 2004-07-06 with total page 736 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book could be a good companion for any graduate student in partial differential equations or in applied mathematics. Each chapter brings indeed new ideas and new techniques which can be used in these fields. The differents chapters can be read independently and are of great pedagogical value. The advanced researcher will find along the book the most recent achievements in various fields. - Independent chapters - Most recent advances in each fields - Hight didactic quality - Self contained - Excellence of the contributors - Wide range of topics

Contributions to Nonlinear Analysis

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Publisher : Springer Science & Business Media
ISBN 13 : 3764374012
Total Pages : 516 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Contributions to Nonlinear Analysis by : Thierry Cazenave

Download or read book Contributions to Nonlinear Analysis written by Thierry Cazenave and published by Springer Science & Business Media. This book was released on 2007-08-10 with total page 516 pages. Available in PDF, EPUB and Kindle. Book excerpt: This paper is concerned with the existence and uniform decay rates of solutions of the waveequation with a sourceterm and subject to nonlinear boundary damping ? ? u ?? u =|u| u in ? ×(0,+?) ? tt ? ? ? ? u=0 on ? ×(0,+?) 0 (1. 1) ? ? u+g(u)=0 on ? ×(0,+?) ? t 1 ? ? ? ? 0 1 u(x,0) = u (x); u (x,0) = u (x),x? ? , t n where ? is a bounded domain of R ,n? 1, with a smooth boundary ? = ? ?? . 0 1 Here, ? and ? are closed and disjoint and ? represents the unit outward normal 0 1 to ?. Problems like (1. 1), more precisely, ? u ?? u =?f (u)in? ×(0,+?) ? tt 0 ? ? ? ? u=0 on ? ×(0,+?) 0 (1. 2) ? ? u =?g(u )?f (u)on? ×(0,+?) ? t 1 1 ? ? ? ? 0 1 u(x,0) = u (x); u (x,0) = u (x),x? ? , t were widely studied in the literature, mainly when f =0,see[6,13,22]anda 1 long list of references therein. When f =0and f = 0 this kind of problem was 0 1 well studied by Lasiecka and Tataru [15] for a very general model of nonlinear functions f (s),i=0,1, but assuming that f (s)s? 0, that is, f represents, for i i i each i, an attractive force.

Methods on Nonlinear Elliptic Equations

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Publisher :
ISBN 13 : 9781601330062
Total Pages : 0 pages
Book Rating : 4.3/5 (3 download)

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Book Synopsis Methods on Nonlinear Elliptic Equations by : Wenxiong Chen

Download or read book Methods on Nonlinear Elliptic Equations written by Wenxiong Chen and published by . This book was released on 2010 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: