Singularly perturbed methods for nonlinear elliptic problems, Cao, Daomin (chinese Academy Of Sciences, Beijing) Peng, Shuangjie Yan, Shusen
Автор: K. W. Chang; F. A. Howes Название: Nonlinear Singular Perturbation Phenomena ISBN: 038796066X ISBN-13(EAN): 9780387960661 Издательство: Springer Рейтинг: Цена: 88500.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The presentation involves a study of both scalar and vector boundary value problems for ordinary dif- ferential equations, by means of the consistent use of differential in- equality techniques.
Автор: Vladimir Maz`ya; B. Plamenevskij; Serguei Nazarov; Название: Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains Volume II ISBN: 3764363983 ISBN-13(EAN): 9783764363987 Издательство: Springer Рейтинг: Цена: 195610.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: For the first time in the mathematical literature, this two-volume work introduces a unified and general approach to the subject. To a large extent, the book is based on the authors` work, and has no significant overlap with other books on the theory of elliptic boundary value problems
Автор: Vladimir Maz`ya; Serguei Nazarov; Boris Plamenevsk Название: Asymptotic Theory of Elliptic Boundary Value Problems in Singularly Perturbed Domains ISBN: 3764363975 ISBN-13(EAN): 9783764363970 Издательство: Springer Рейтинг: Цена: 195610.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: For the first time in the mathematical literature, this two-volume work introduces a unified and general approach to the subject. To a large extent, the book is based on the authors` work, and has no significant overlap with other books on the theory of elliptic boundary value problems.
Автор: Kelei Wang Название: Free Boundary Problems and Asymptotic Behavior of Singularly Perturbed Partial Differential Equations ISBN: 364244248X ISBN-13(EAN): 9783642442483 Издательство: Springer Рейтинг: Цена: 102480.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: The results of this exceptional thesis on free boundary problems in singularly perturbed PDEs develop our understanding of the effects of strong competition between species. The research has a wealth of valuable applications in both physics and biology.
Автор: Hans-G?rg Roos; Martin Stynes; Lutz Tobiska Название: Robust Numerical Methods for Singularly Perturbed Differential Equations ISBN: 3642070825 ISBN-13(EAN): 9783642070822 Издательство: Springer Рейтинг: Цена: 135090.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This new edition incorporates new developments in numerical methods for singularly perturbed differential equations, focusing on linear convection-diffusion equations and on nonlinear flow problems that appear in computational fluid dynamics.
Автор: Emmanuel Fr?nod Название: Two-Scale Approach to Oscillatory Singularly Perturbed Transport Equations ISBN: 3319646672 ISBN-13(EAN): 9783319646671 Издательство: Springer Рейтинг: Цена: 32600.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: In addition, it explores the homogenization of hyperbolic partial differential equations with oscillating coefficients and linear oscillatory singularly perturbed hyperbolic partial differential equations.
Автор: Folkmar Bornemann Название: Homogenization in Time of Singularly Perturbed Mechanical Systems ISBN: 3540644474 ISBN-13(EAN): 9783540644477 Издательство: Springer Рейтинг: Цена: 27910.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: This text is about the elimination of fast oscillatory scales in dynamical systems, which is important for efficient computer-simulations and the understanding of model hierarchies. The author presents his method, homogenization in time, based on energy principles and weak convergence techniques.
Автор: Charles Li; Stephen Wiggins Название: Invariant Manifolds and Fibrations for Perturbed Nonlinear Schr?dinger Equations ISBN: 0387949259 ISBN-13(EAN): 9780387949253 Издательство: Springer Рейтинг: Цена: 121110.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: In this monograph the authors present detailed and pedagogic proofs of persistence theorems for normally hyperbolic invariant manifolds and their stable and unstable manifolds for classes of perturbations of the NLS equation, as well as for the existence and persistence of fibrations of these invariant manifolds.
Автор: Charles Li; Stephen Wiggins Название: Invariant Manifolds and Fibrations for Perturbed Nonlinear Schr?dinger Equations ISBN: 1461273072 ISBN-13(EAN): 9781461273073 Издательство: Springer Рейтинг: Цена: 46570.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: In this monograph the authors present detailed and pedagogic proofs of persistence theorems for normally hyperbolic invariant manifolds and their stable and unstable manifolds for classes of perturbations of the NLS equation, as well as for the existence and persistence of fibrations of these invariant manifolds.
This book elaborates on an idea put forward by M. Abouzaid on equipping the Morse cochain complex of a smooth Morse function on a closed oriented manifold with the structure of an A?-algebra by means of perturbed gradient flow trajectories. This approach is a variation on K. Fukaya’s definition of Morse-A?-categories for closed oriented manifolds involving families of Morse functions. To make A?-structures in Morse theory accessible to a broader audience, this book provides a coherent and detailed treatment of Abouzaid’s approach, including a discussion of all relevant analytic notions and results, requiring only a basic grasp of Morse theory. In particular, no advanced algebra skills are required, and the perturbation theory for Morse trajectories is completely self-contained.
In addition to its relevance for finite-dimensional Morse homology, this book may be used as a preparation for the study of Fukaya categories in symplectic geometry. It will be of interest to researchers in mathematics (geometry and topology), and to graduate students in mathematics with a basic command of the Morse theory.
Автор: Alexander A. Kovalevsky, Igor I. Skrypnik, Andrey E. Shishkov Название: Singular Solutions of Nonlinear Elliptic and Parabolic Equations ISBN: 3110315483 ISBN-13(EAN): 9783110315486 Издательство: Walter de Gruyter Цена: 223090.00 T Наличие на складе: Есть у поставщика Поставка под заказ. Описание: 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:ForewordPart I: Nonlinear elliptic equations with L^1-dataNonlinear elliptic equations of the second order with L^1-dataNonlinear equations of the fourth order with strengthened coercivity and L^1-dataPart II: Removability of singularities of the solutions of quasilinear elliptic and parabolic equations of the second orderRemovability of singularities of the solutions of quasilinear elliptic equationsRemovability of singularities of the solutions of quasilinear parabolic equationsQuasilinear elliptic equations with coefficients from the Kato classPart III: Boundary regimes with peaking for quasilinear parabolic equationsEnergy methods for the investigation of localized regimes with peaking for parabolic second-order equationsMethod of functional inequalities in peaking regimes for parabolic equations of higher ordersNonlocalized regimes with singular peakingAppendix: Formulations and proofs of the auxiliary resultsBibliography
This book is devoted to the study of elliptic second-order degenerate quasilinear equations, the model of which is the p-Laplacian, with or without dominant lower order reaction term. Emphasis is put on three aspects:
The existence of separable singular solutions enables the description of isolated singularities of general solutions. The construction of singular solutions is delicate and cannot be done without the understanding of the spherical p-harmonic eigenvalue problem.
When the equations are considered on a Riemannian manifold, existence or non-existence of solutions depends on geometric assumptions such as the curvature. A priori estimates and Liouville type problems are analyzed.
When the equations are considered with a forcing term in the class of measures, their study is strongly linked to the properties of a class of potentials appearing in harmonic analysis such as the Riesz, the Bessel or the Wolff potentials and to their associated capacities. Necessary and sufficient conditions for existence of solutions link the continuity of the measure with respect to some appropriate capacity.
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