Описание: The book provides a comprehensive exposition of modern topics in nonlinear analysis with applications to various boundary value problems with discontinuous nonlinearities and nonsmooth constraints. Our framework includes multivalued elliptic problems with discontinuities, variational inequalities, hemivariational inequalities and evolution problems. In addition to the existence of solutions, a major part of the book is devoted to the study of different qualitative properties such as multiplicity, location, extremality, and stability. The treatment relies on variational methods, monotonicity principles, topological arguments and optimization techniques. The book is based on the authors' original results obtained in the last decade. A great deal of the material is published for the first time in this book and is organized in a unifying way. The book is self-contained. The abstract results are illustrated through various examples and applications.
Автор: David L. Powers Название: Boundary Value Problems, ISBN: 0123747198 ISBN-13(EAN): 9780123747198 Издательство: Elsevier Science Рейтинг: Цена: 12845 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Boundary Value Problems, Sixth Edition, is the leading text on boundary value problems and Fourier series for professionals and students in engineering, science, and mathematics who work with partial differential equations. In this updated edition, author David Powers provides a thorough overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. Additional techniques used include Laplace transform and numerical methods. The book contains nearly 900 exercises ranging in difficulty from basic drills to advanced problem-solving exercises. Professors and students agree that Powers is a master at creating examples and exercises that skillfully illustrate the techniques used to solve science and engineering problems.
Автор: J. T. Wloka Название: Boundary Value Problems for Elliptic Systems ISBN: 0521061431 ISBN-13(EAN): 9780521061438 Издательство: Cambridge Academ Рейтинг: Цена: 7952 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: This book examines the theory of boundary value problems for elliptic systems of partial differential equations, a theory which has many applications in mathematics and the physical sciences. The aim is to ‘algebraise’ the index theory by means of pseudo-differential operators and new methods in the spectral theory of matrix polynomials. This latter theory provides important tools that will enable the student to work efficiently with the principal symbols of the elliptic and boundary operators on the boundary. This book is ideal for use in graduate level courses on partial differential equations, elliptic systems, pseudo-differential operators and matrix analysis. Since many new methods and results are introduced and used throughout the book, all the theorems are proved in detail, and the methods are well illustrated through numerous examples and exercises.
Описание: Perturbation of the boundary is a rather neglected topic in the study of PDEs for two main reasons. First, on the surface it appears trivial, merely a change of variables and an application of the chain rule. Second, carrying out such a change of variables frequently results in long and difficult calculations. Here the author carefully discusses a calculus that allows the computational morass to be bypassed, and he goes on to develop more general forms of standard theorems, which help answer a wide range of problems involving boundary perturbations. Many examples are presented to demonstrate the usefulness of the author’s approach, while on the other hand many tantalizing open questions remain. Anyone whose research involves PDEs will find something of interest in this book.
Автор: Wendland Wolfgang, Hsiao George C. Название: Integral Equation Methods for Boundary Value Problems ISBN: 3540152849 ISBN-13(EAN): 9783540152842 Издательство: Springer Рейтинг: Цена: 19304 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Describes basic mathematical properties of solutions to boundary integral equations and presents a systematic approach to the variational methods for the boundary integral equations arising in elasticity, fluid mechanics, and acoustic scattering theory.
Автор: Pelloni Название: Unified Transform for Boundary Value Problems ISBN: 1611973813 ISBN-13(EAN): 9781611973815 Издательство: Eurospan Рейтинг: Цена: 18636 р. Наличие на складе: Нет в наличии.
Описание: This book describes state-of-the-art advances and applications of the unified transform and its relation to the boundary element method. The authors present the solution of boundary value problems from several different perspectives, in particular the type of problems modeled by partial differential equations (PDEs). They discuss recent applications of the unified transform to the analysis and numerical modeling of boundary value problems for linear and integrable nonlinear PDEs and the closely related boundary element method, a well-established numerical approach for solving linear elliptic PDEs.The text is divided into three parts. Part I contains new theoretical results on linear and nonlinear evolutionary and elliptic problems. New explicit solution representations for several classes of boundary value problems are constructed and rigorously analyzed. Part II is a detailed overview of variational formulations for elliptic problems. It places the unified transform approach in a classic context alongside the boundary element method and stresses its novelty. Part III presents recent numerical applications based on the boundary element method and on the unified transform.
Описание: Computational Fluid Dynamics Based on the Unified Coordinates reviews the relative advantages and drawbacks of Eulerian and Lagrangian coordinates as well as the Arbitrary Lagrangian-Eulerian (ALE) and various moving mesh methods in Computational Fluid Dynamics (CFD) for one- and multi-dimensional flows. It then systematically introduces the unified coordinate approach to CFD, illustrated with numerous examples and comparisons to clarify its relation with existing approaches. The book is intended for researchers, graduate students and practitioners in the field of Computational Fluid Dynamics. Emeritus Professor Wai-Hou Hui and Professor Kun Xu both work at the Department of Mathematics of the Hong Kong University of Science & Technology, Hong Kong, China.
Автор: Graef John R., Kong Lingju Название: Multiple Solutions of Boundary Value Problems: A Variational Approach ISBN: 9814696544 ISBN-13(EAN): 9789814696548 Издательство: World Scientific Publishing Рейтинг: Цена: 15908 р. Наличие на складе: Есть у поставщика Поставка под заказ.
Описание: Variational Methods And Their Generalizations Have Been Verified To Be Useful Tools In Proving The Existence Of Solutions To A Variety Of Boundary Value Problems For Ordinary, Impulsive, And Partial Differential Equations As Well As For Difference Equations. In This Monograph, We Look At How Variational Methods Can Be Used In All These Settings. In Our First Chapter, We Gather The Basic Notions And Fundamental Theorems That Will Be Applied In The Remainder Of This Monograph. 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 The Sturm–Liouville Problems, Multi-Point Boundary Value Problems, Problems With Impulses, Partial Differential Equations, And Difference Equations. An Extensive Bibliography Is Also Included.
Описание: Provides information on the qualitative theory of elliptic boundary value problems for linear and quasilinear second order equations in non-smooth domains. This book presents such results as: sharp estimates for strong and weak solutions, solvability of boundary value problems, regularity assertions for solutions near singular points, and more.
Описание: Introduces the method of lower and upper solutions for ordinary differential equations. Divided into two sections, this book presents the fundamental features of the method. It also pays attention to other settings such as partial differential equations or functional differential equations. It features illustrated theorems by examples.
Описание: This revision of the market-leading book maintains its classic strengths: contemporary approach, flexible chapter construction, clear exposition, and outstanding problems. Like its predessors, this revision is written from the viewpoint of the applied mathematician, focusing both on the theory and the practical applications of Differential Equations as they apply to engineering and the sciences. Sound and Accurate Exposition of Theory - special attention is made to methods of solution, analysis, and approximation. Use of technology, illustrations, and problem sets help readers develop an intuitive understanding of the material. Historical footnotes trace development of the discipline and identify outstanding individual contributions.
Автор: David L. Powers Название: Boundary Value Problems, 5th edition ISBN: 0125637381 ISBN-13(EAN): 9780125637381 Издательство: Elsevier Science Цена: 12170 р. Наличие на складе: Невозможна поставка.
Описание: Deals with boundary value problems and Fourier series. This book offers a theoretical overview of solving boundary value problems involving partial differential equations by the methods of separation of variables. It includes a CD with animations and graphics of solutions, exercises and chapter review questions, and nearly 900 exercises.
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