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On The Growth Of Solutions Of Non Linear Elliptic Partial Differential Equations
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Book Synopsis Elliptic Partial Differential Equations by : Lucio Boccardo
Download or read book Elliptic Partial Differential Equations written by Lucio Boccardo and published by Walter de Gruyter. This book was released on 2013-10-29 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elliptic partial differential equations is one of the main and most active areas in mathematics. This book is devoted to the study of linear and nonlinear elliptic problems in divergence form, with the aim of providing classical results, as well as more recent developments about distributional solutions. For this reason this monograph is addressed to master's students, PhD students and anyone who wants to begin research in this mathematical field.
Book Synopsis Nonlinear Elliptic Partial Differential Equations by : Hervé Le Dret
Download or read book Nonlinear Elliptic Partial Differential Equations written by Hervé Le Dret and published by Springer. This book was released on 2018-05-25 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook presents the essential parts of the modern theory of nonlinear partial differential equations, including the calculus of variations. After a short review of results in real and functional analysis, the author introduces the main mathematical techniques for solving both semilinear and quasilinear elliptic PDEs, and the associated boundary value problems. Key topics include infinite dimensional fixed point methods, the Galerkin method, the maximum principle, elliptic regularity, and the calculus of variations. Aimed at graduate students and researchers, this textbook contains numerous examples and exercises and provides several comments and suggestions for further study.
Book Synopsis On the Growth of Solutions of Non-linear Elliptic Partial Differential Equations by : Robert Finn
Download or read book On the Growth of Solutions of Non-linear Elliptic Partial Differential Equations written by Robert Finn and published by . This book was released on 1954 with total page 44 pages. Available in PDF, EPUB and Kindle. Book excerpt: An analogue of Schwar'z Lemma is proved for the solutions of a class of non-linear partial differential equations, which includes equations derived by suitable approximation to the adiabatic gas law.
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.
Book Synopsis Nonlinear Elliptic Partial Differential Equations by : J. P. Gossez
Download or read book Nonlinear Elliptic Partial Differential Equations written by J. P. Gossez and published by American Mathematical Soc.. This book was released on 2011 with total page 278 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains papers on semi-linear and quasi-linear elliptic equations from the workshop on Nonlinear Elliptic Partial Differential Equations, in honor of Jean-Pierre Gossez's 65th birthday, held September 2-4, 2009 at the Universite Libre de Bruxelles, Belgium. The workshop reflected Gossez's contributions in nonlinear elliptic PDEs and provided an opening to new directions in this very active research area. Presentations covered recent progress in Gossez's favorite topics, namely various problems related to the $p$-Laplacian operator, the antimaximum principle, the Fucik Spectrum, and other related subjects. This volume will be of principle interest to researchers in nonlinear analysis, especially in partial differential equations of elliptic type.
Book Synopsis Nonlinear Problems with Lack of Compactness by : Giovanni Molica Bisci
Download or read book Nonlinear Problems with Lack of Compactness written by Giovanni Molica Bisci and published by Walter de Gruyter GmbH & Co KG. This book was released on 2021-02-08 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative book presents recent research results on nonlinear problems with lack of compactness. The topics covered include several nonlinear problems in the Euclidean setting as well as variational problems on manifolds. The combination of deep techniques in nonlinear analysis with applications to a variety of problems make this work an essential source of information for researchers and graduate students working in analysis and PDE's.
Book Synopsis Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48) by : Kari Astala
Download or read book Elliptic Partial Differential Equations and Quasiconformal Mappings in the Plane (PMS-48) written by Kari Astala and published by Princeton University Press. This book was released on 2009-01-18 with total page 708 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the most recent developments in the theory of planar quasiconformal mappings with a particular focus on the interactions with partial differential equations and nonlinear analysis. It gives a thorough and modern approach to the classical theory and presents important and compelling applications across a spectrum of mathematics: dynamical systems, singular integral operators, inverse problems, the geometry of mappings, and the calculus of variations. It also gives an account of recent advances in harmonic analysis and their applications in the geometric theory of mappings. The book explains that the existence, regularity, and singular set structures for second-order divergence-type equations--the most important class of PDEs in applications--are determined by the mathematics underpinning the geometry, structure, and dimension of fractal sets; moduli spaces of Riemann surfaces; and conformal dynamical systems. These topics are inextricably linked by the theory of quasiconformal mappings. Further, the interplay between them allows the authors to extend classical results to more general settings for wider applicability, providing new and often optimal answers to questions of existence, regularity, and geometric properties of solutions to nonlinear systems in both elliptic and degenerate elliptic settings.
Book Synopsis Partial Differential Equations by : Walter A. Strauss
Download or read book Partial Differential Equations written by Walter A. Strauss and published by John Wiley & Sons. This book was released on 2007-12-21 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
Book Synopsis Nonlinear Systems Of Partial Differential Equations: Applications To Life And Physical Sciences by : Anthony W Leung
Download or read book Nonlinear Systems Of Partial Differential Equations: Applications To Life And Physical Sciences written by Anthony W Leung and published by World Scientific. This book was released on 2009-08-28 with total page 545 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Nonlinear Parabolic Equations by : Lucio Boccardo
Download or read book Nonlinear Parabolic Equations written by Lucio Boccardo and published by Longman Scientific and Technical. This book was released on 1987 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Chebyshev and Fourier Spectral Methods by : John P. Boyd
Download or read book Chebyshev and Fourier Spectral Methods written by John P. Boyd and published by Courier Corporation. This book was released on 2001-12-03 with total page 690 pages. Available in PDF, EPUB and Kindle. Book excerpt: Completely revised text focuses on use of spectral methods to solve boundary value, eigenvalue, and time-dependent problems, but also covers Hermite, Laguerre, rational Chebyshev, sinc, and spherical harmonic functions, as well as cardinal functions, linear eigenvalue problems, matrix-solving methods, coordinate transformations, methods for unbounded intervals, spherical and cylindrical geometry, and much more. 7 Appendices. Glossary. Bibliography. Index. Over 160 text figures.
Book Synopsis Singular Solutions of Nonlinear Elliptic and Parabolic Equations by : Alexander A. Kovalevsky
Download or read book Singular Solutions of Nonlinear Elliptic and Parabolic Equations written by Alexander A. Kovalevsky and published by Walter de Gruyter GmbH & Co KG. This book was released on 2016-03-21 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph looks at several trends in the investigation of singular solutions of nonlinear elliptic and parabolic equations. It discusses results on the existence and properties of weak and entropy solutions for elliptic second-order equations and some classes of fourth-order equations with L1-data and questions on the removability of singularities of solutions to elliptic and parabolic second-order equations in divergence form. It looks at localized and nonlocalized singularly peaking boundary regimes for different classes of quasilinear parabolic second- and high-order equations in divergence form. The book will be useful for researchers and post-graduate students that specialize in the field of the theory of partial differential equations and nonlinear analysis. Contents: Foreword Part I: Nonlinear elliptic equations with L^1-data Nonlinear elliptic equations of the second order with L^1-data Nonlinear equations of the fourth order with strengthened coercivity and L^1-data Part II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second order Removability of singularities of the solutions of quasilinear elliptic equations Removability of singularities of the solutions of quasilinear parabolic equations Quasilinear elliptic equations with coefficients from the Kato class Part III: Boundary regimes with peaking for quasilinear parabolic equations Energy methods for the investigation of localized regimes with peaking for parabolic second-order equations Method of functional inequalities in peaking regimes for parabolic equations of higher orders Nonlocalized regimes with singular peaking Appendix: Formulations and proofs of the auxiliary results Bibliography
Book Synopsis Nonlinear Partial Differential Equations and Their Applications by :
Download or read book Nonlinear Partial Differential Equations and Their Applications written by and published by . This book was released on 1981 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Partial Differential Equations of Elliptic Type by : C. Miranda
Download or read book Partial Differential Equations of Elliptic Type written by C. Miranda and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 384 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the theory of partial differential equations, the study of elliptic equations occupies a preeminent position, both because of the importance which it assumes for various questions in mathematical physics, and because of the completeness of the results obtained up to the present time. In spite of this, even in the more classical treatises on analysis the theory of elliptic equations has been considered and illustrated only from particular points of view, while the only expositions of the whole theory, the extremely valuable ones by LICHTENSTEIN and AscoLI, have the charac ter of encyclopedia articles and date back to many years ago. Consequently it seemed to me that it would be of some interest to try to give an up-to-date picture of the present state of research in this area in a monograph which, without attaining the dimensions of a treatise, would nevertheless be sufficiently extensive to allow the expo sition, in some cases in summary form, of the various techniques used in the study of these equations.
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 415 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.
Book Synopsis Nonlinear Partial Differential Equations by : W. F. Ames
Download or read book Nonlinear Partial Differential Equations written by W. F. Ames and published by Academic Press. This book was released on 2014-05-12 with total page 335 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nonlinear Partial Differential Equations: A Symposium on Methods of Solution is a collection of papers presented at the seminar on methods of solution for nonlinear partial differential equations, held at the University of Delaware, Newark, Delaware on December 27-29, 1965. The sessions are divided into four Symposia: Analytic Methods, Approximate Methods, Numerical Methods, and Applications. Separating 19 lectures into chapters, this book starts with a presentation of the methods of similarity analysis, particularly considering the merits, advantages and disadvantages of the methods. The subsequent chapters describe the fundamental ideas behind the methods for the solution of partial differential equation derived from the theory of dynamic programming and from finite systems of ordinary differential equations. These topics are followed by reviews of the principles to the lubrication approximation and compressible boundary-layer flow computation. The discussion then shifts to several applications of nonlinear partial differential equations, including in electrical problems, two-phase flow, hydrodynamics, and heat transfer. The remaining chapters cover other solution methods for partial differential equations, such as the synergetic approach. This book will prove useful to applied mathematicians, physicists, and engineers.
Book Synopsis Handbook of Nonlinear Partial Differential Equations by : Andrei D. Polyanin
Download or read book Handbook of Nonlinear Partial Differential Equations written by Andrei D. Polyanin and published by CRC Press. This book was released on 2004-06-02 with total page 835 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Handbook of Nonlinear Partial Differential Equations is the latest in a series of acclaimed handbooks by these authors and presents exact solutions of more than 1600 nonlinear equations encountered in science and engineering--many more than any other book available. The equations include those of parabolic, hyperbolic, elliptic and other types, and the authors pay special attention to equations of general form that involve arbitrary functions. A supplement at the end of the book discusses the classical and new methods for constructing exact solutions to nonlinear equations. To accommodate different mathematical backgrounds, the authors avoid wherever possible the use of special terminology, outline some of the methods in a schematic, simplified manner, and arrange the equations in increasing order of complexity. Highlights of the Handbook:
