Morse Index of Solutions of Nonlinear Elliptic Equations, Lucio Damascelli, Filomena Pacella
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: 33463.00 р. 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
Описание: This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.
Автор: Dret, Herve Le Название: Nonlinear elliptic partial differential equations ISBN: 3319783890 ISBN-13(EAN): 9783319783895 Издательство: Springer Рейтинг: Цена: 9083.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: 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.
Описание: This book deals with a systematic study of a dynamical system approach to investigate the symmetrization and stabilization properties of nonnegative solutions of nonlinear elliptic problems in asymptotically symmetric unbounded domains. The usage of infinite dimensional dynamical systems methods for elliptic problems in unbounded domains as well as finite dimensional reduction of their dynamics requires new ideas and tools. To this end, both a trajectory dynamical systems approach and new Liouville type results for the solutions of some class of elliptic equations are used. The work also uses symmetry and monotonicity results for nonnegative solutions in order to characterize an asymptotic profile of solutions and compares a pure elliptic partial differential equations approach and a dynamical systems approach. The new results obtained will be particularly useful for mathematical biologists.
Variational methods are very powerful techniques in nonlinear analysis and are extensively used in many disciplines of pure and applied mathematics (including ordinary and partial differential equations, mathematical physics, gauge theory, and geometrical analysis).
In our first chapter, we gather the basic notions and fundamental theorems that will be applied throughout the chapters. While many of these items are easily available in the literature, we gather them here both for the convenience of the reader and for the purpose of making this volume somewhat self-contained. Subsequent chapters deal with how variational methods can be used in fourth-order problems, Kirchhoff problems, nonlinear field problems, gradient systems, and variable exponent problems. A very extensive bibliography is also included.
Автор: Boling Guo, Dongfen Bian, Fangfang Li, Xiaoyu Xi Название: Vanishing Viscosity Method: Solutions to Nonlinear Systems ISBN: 3110495287 ISBN-13(EAN): 9783110495287 Издательство: Walter de Gruyter Рейтинг: Цена: 26024.00 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание:
The book summarizes several mathematical aspects of the vanishing viscosity method and considers its applications in studying dynamical systems such as dissipative systems, hyperbolic conversion systems and nonlinear dispersion systems. Including original research results, the book demonstrates how to use such methods to solve PDEs and is an essential reference for mathematicians, physicists and engineers working in nonlinear science.
Contents: Preface Sobolev Space and Preliminaries The Vanishing Viscosity Method of Some Nonlinear Evolution System The Vanishing Viscosity Method of Quasilinear Hyperbolic System Physical Viscosity and Viscosity of Difference Scheme Convergence of Lax-Friedrichs Scheme, Godunov Scheme and Glimm Scheme Electric-Magnetohydrodynamic Equations References
Описание: With a pedagogic format ideal for graduate students, this text includes a wealth of examples focusing on solutions in dynamical systems theory that mirror those used in Lyapunov`s first method, tackling ordinary differential equations expressed as series form.
Описание: Presents an account of the state of algebraic-theoretic methods as applied to linear and nonlinear multidimensional equations of mathematical and theoretical physics. This volume studies the symmetry of integro-differential equations and describes the method of finding final nonlocal transformations.
Описание: The goals of this text are to prove or disprove the solution of reduced nonlinear ODE`s by different analytic methods, and to show that these solutions are intermediate asymptotics of a class of initial/boundary conditions arising from physical considerations.
Описание: Mathematical Notes, 29 Originally published in 1983. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paper
Описание: Engineering applications offer benefits and opportunities across a range of different industries and fields. By developing effective methods of analysis, results and solutions are produced with higher accuracy.Numerical and Analytical Solutions for Solving Nonlinear Equations in Heat Transfer is an innovative source of academic research on the optimized techniques for analyzing heat transfer equations and the application of these methods across various fields. Highlighting pertinent topics such as the differential transformation method, industrial applications, and the homotopy perturbation method, this book is ideally designed for engineers, researchers, graduate students, professionals, and academics interested in applying new mathematical techniques in engineering sciences.Topics Covered:Adomian Decomposition MethodDifferential Transformation MethodHomotopy Analysis MethodHomotopy Perturbation MethodIndustrial applicationsVariational Iteration Method
Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics is the first book to provide a systematic construction of exact solutions via linear invariant subspaces for nonlinear differential operators. Acting as a guide to nonlinear evolution equations and models from physics and mechanics, the book focuses on the existence of new exact solutions on linear invariant subspaces for nonlinear operators and their crucial new properties.
This practical reference deals with various partial differential equations (PDEs) and models that exhibit some common nonlinear invariant features. It begins with classical as well as more recent examples of solutions on invariant subspaces. In the remainder of the book, the authors develop several techniques for constructing exact solutions of various nonlinear PDEs, including reaction-diffusion and gas dynamics models, thin-film and Kuramoto-Sivashinsky equations, nonlinear dispersion (compacton) equations, KdV-type and Harry Dym models, quasilinear magma equations, and Green-Naghdi equations. Using exact solutions, they describe the evolution properties of blow-up or extinction phenomena, finite interface propagation, and the oscillatory, changing sign behavior of weak solutions near interfaces for nonlinear PDEs of various types and orders. The techniques surveyed in Exact Solutions and Invariant Subspaces of Nonlinear Partial Differential Equations in Mechanics and Physics serve as a preliminary introduction to the general theory of nonlinear evolution PDEs of different orders and types.
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