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Singular Solutions For Some Semilinear Elliptic Equations
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Book Synopsis Singular Solutions for Some Semilinear Elliptic Equations by : Haim Brezis
Download or read book Singular Solutions for Some Semilinear Elliptic Equations written by Haim Brezis and published by . This book was released on 1985 with total page 20 pages. Available in PDF, EPUB and Kindle. Book excerpt: This document gives a new proof of Veron's result concerning the classification of isolated singularities for the equation-delta u + u sub p = 0. The author also establish that the singular behavior at a point can be prescribed and determines uniquely the solution (under fixed boundary conditions). Keywords: Nonlinear Elliptic equations; Scaling; Applied mathematics; Mathematical analysis. (Author).
Book Synopsis Global Solution Curves For Semilinear Elliptic Equations by : Philip Korman
Download or read book Global Solution Curves For Semilinear Elliptic Equations written by Philip Korman and published by World Scientific. This book was released on 2012-02-10 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented.The author is one of the original contributors to the field of exact multiplicity results.
Book Synopsis Global Solution Curves for Semilinear Elliptic Equations by : Philip Korman
Download or read book Global Solution Curves for Semilinear Elliptic Equations written by Philip Korman and published by World Scientific. This book was released on 2012 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the bifurcation theory approach to global solution curves and studies the exact multiplicity of solutions for semilinear Dirichlet problems, aiming to obtain a complete understanding of the solution set. This understanding opens the way to efficient computation of all solutions. Detailed results are obtained in case of circular domains, and some results for general domains are also presented. The author is one of the original contributors to the field of exact multiplicity results.
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 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 2011-08-11 with total page 618 pages. Available in PDF, EPUB and Kindle. Book excerpt: This handbook is the sixth and last volume in the series devoted to stationary partial differential equations. The topics covered by this volume include in particular domain perturbations for boundary value problems, singular solutions of semilinear elliptic problems, positive solutions to elliptic equations on unbounded domains, symmetry of solutions, stationary compressible Navier-Stokes equation, Lotka-Volterra systems with cross-diffusion, and fixed point theory for elliptic boundary value problems. * Collection of self-contained, state-of-the-art surveys * Written by well-known experts in the field * Informs and updates on all the latest developments
Book Synopsis Semilinear Elliptic Equations by : Takashi Suzuki
Download or read book Semilinear Elliptic Equations written by Takashi Suzuki and published by Walter de Gruyter GmbH & Co KG. This book was released on 2020-10-12 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: This authoritative monograph presents in detail classical and modern methods for the study of semilinear elliptic equations, that is, methods to study the qualitative properties of solutions using variational techniques, the maximum principle, blowup analysis, spectral theory, topological methods, etc. The book is self-contained and is addressed to experienced and beginning researchers alike.
Download or read book NPS-MA-91-001 written by Aihua W. Shaker and published by . This book was released on 1991* with total page 9 pages. Available in PDF, EPUB and Kindle. Book excerpt: We study the singular semilinear elliptic equation. This type of equation arises in the boundary layer theory of viscous fluids. From the results it follows that the equation has a unique classical solution within a bounded domain omega, where p(x) is a sufficiently regular function which is positive on omega. Kusano and Swanson gave the existence proof on exterior domains. In this paper we show via the upper and lower solution method, which is also referred to as the barrier method, that the equation has a bounded positive entire solution vanishing at infinity. It is observed by Callegari, Friedman and Nachman that if the partial differential equations describing the boundary layer behind a rarefaction or shock wave (with viscosity proportional to the temperature) traveling down, and perpendicular to, a flat plate are written in terms of a stream function and a similarity variable the following Blasius-type equation emerges.
Book Synopsis Semilinear Elliptic Equations for Beginners by : Marino Badiale
Download or read book Semilinear Elliptic Equations for Beginners written by Marino Badiale and published by Springer Science & Business Media. This book was released on 2010-12-07 with total page 204 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semilinear elliptic equations are of fundamental importance for the study of geometry, physics, mechanics, engineering and life sciences. The variational approach to these equations has experienced spectacular success in recent years, reaching a high level of complexity and refinement, with a multitude of applications. Additionally, some of the simplest variational methods are evolving as classical tools in the field of nonlinear differential equations. This book is an introduction to variational methods and their applications to semilinear elliptic problems. Providing a comprehensive overview on the subject, this book will support both student and teacher engaged in a first course in nonlinear elliptic equations. The material is introduced gradually, and in some cases redundancy is added to stress the fundamental steps in theory-building. Topics include differential calculus for functionals, linear theory, and existence theorems by minimization techniques and min-max procedures. Requiring a basic knowledge of Analysis, Functional Analysis and the most common function spaces, such as Lebesgue and Sobolev spaces, this book will be of primary use to graduate students based in the field of nonlinear partial differential equations. It will also serve as valuable reading for final year undergraduates seeking to learn about basic working tools from variational methods and the management of certain types of nonlinear problems.
Book Synopsis Variational Methods by : Michael Struwe
Download or read book Variational Methods written by Michael Struwe and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hilbert's talk at the second International Congress of 1900 in Paris marked the beginning of a new era in the calculus of variations. A development began which, within a few decades, brought tremendous success, highlighted by the 1929 theorem of Ljusternik and Schnirelman on the existence of three distinct prime closed geodesics on any compact surface of genus zero, and the 1930/31 solution of Plateau's problem by Douglas and Radò. The book gives a concise introduction to variational methods and presents an overview of areas of current research in this field. This new edition has been substantially enlarged, a new chapter on the Yamabe problem has been added and the references have been updated. All topics are illustrated by carefully chosen examples, representing the current state of the art in their field.
Book Synopsis Entire Solutions of Semilinear Elliptic Equations by : Ilya Kuzin
Download or read book Entire Solutions of Semilinear Elliptic Equations written by Ilya Kuzin and published by Birkhauser. This book was released on 1997 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semilinear elliptic equations play an important role in many areas of mathematics and its applications to physics and other sciences. This book presents a wealth of modern methods to solve such equations, including the systematic use of the Pohozaev identities for the description of sharp estimates for radial solutions and the fibring method. Existence results for equations with supercritical growth and non-zero right-hand sides are given.Readers of this exposition will be advanced students and researchers in mathematics, physics and other sciences who want to learn about specific methods to tackle problems involving semilinear elliptic equations.
Book Synopsis Entire Solutions of Semilinear Elliptic Equations by : Ilya A. Kuzin
Download or read book Entire Solutions of Semilinear Elliptic Equations written by Ilya A. Kuzin and published by Birkhäuser. This book was released on 2012-01-06 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Semilinear elliptic equations play an important role in many areas of mathematics and its applications to other sciences. This book presents a wealth of modern methods to solve such equations. Readers of this exposition will be advanced students and researchers in mathematics, physics and other.
Book Synopsis Semilinear Elliptic Equations by : Takashi Suzuki
Download or read book Semilinear Elliptic Equations written by Takashi Suzuki and published by . This book was released on 1994 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Advances in Geometric Analysis by : Stanislaw Janeczko
Download or read book Advances in Geometric Analysis written by Stanislaw Janeczko and published by . This book was released on 2012 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: Covers some of the most recent and important developments in geometry and theoretical physics today. Topics include Monge-Ampère equations, Kähler-Ricci flows, and other fully non-linear elliptic and parabolic equations; canonical metrics in Kähler geometry; notions of quasi-local mass in general relativity and geometric properties of gauge theories; and new algebro-geometric and symplectic methods.
Book Synopsis Positive Solutions of Some Systems of Semilinear Elliptic Equations by : J. A. Blat-Gimeno
Download or read book Positive Solutions of Some Systems of Semilinear Elliptic Equations written by J. A. Blat-Gimeno and published by . This book was released on 1984 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Semilinear Elliptic Equations for Beginners by : Qing Jun Hou
Download or read book Semilinear Elliptic Equations for Beginners written by Qing Jun Hou and published by . This book was released on 2016-08-01 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: Elliptic equation is a class of partial differential equations describing phenomena that do not change from moment to moment, as when a flow of heat or fluid takes place within a medium with no accumulations. The Laplace equation, uxx + uyy = 0, is the simplest such equation describing this condition in two dimensions. In addition to satisfying a differential equation within the region, the elliptic equation is also determined by its values (boundary values) along the boundary of the region, which represent the effect from outside the region. Semilinear elliptic equations play an important role in many areas of mathematics and its applications to other sciences. Semilinear elliptic equations are of fundamental importance for the study of geometry, physics, mechanics, engineering and life sciences. The variational approach to these equations has experienced spectacular success in recent years, reaching a high level of complexity and refinement, with a multitude of applications. Semilinear Elliptic Equations for Beginners is a comprehensive guide to variational methods and their applications to semilinear elliptic problems. This book deals with nonlinear boundary value problems for semilinear elliptic equations on unbounded domains. This book will be of valuable for professors, practitioners, and researchers in mathematics and mathematical physics.
Book Synopsis Computation of Singular Solutions in Elliptic Problems and Elasticity by : D. Leguillon
Download or read book Computation of Singular Solutions in Elliptic Problems and Elasticity written by D. Leguillon and published by John Wiley & Sons. This book was released on 1987 with total page 208 pages. Available in PDF, EPUB and Kindle. Book excerpt: The stress field in composite elastic media often contains singularities, in particular at the intersections of interfaces with boundaries. This book describes two new methods of computing the eigenvalues and eigenvectors of singularities, leading to a full description of their structure.
Book Synopsis Nonlinear Evolution Equations and Related Topics by : Wolfgang Arendt
Download or read book Nonlinear Evolution Equations and Related Topics written by Wolfgang Arendt and published by Birkhäuser. This book was released on 2012-12-06 with total page 803 pages. Available in PDF, EPUB and Kindle. Book excerpt: Philippe Bénilan was a most original and charismatic mathematician who had a deep and decisive impact on the theory of Nonlinear Evolution Equations. Dedicated to him, Nonlinear Evolution Equations and Related Topics contains research papers written by highly distinguished mathematicians. They are all related to Philippe Benilan's work and reflect the present state of this most active field. The contributions cover a wide range of nonlinear and linear equations.
