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.
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.
Автор: Dean G. Duffy Название: Mixed Boundary Value Problems ISBN: 1584885793 ISBN-13(EAN): 9781584885795 Издательство: Taylor&Francis Рейтинг: Цена: 11495 р. Наличие на складе: Невозможна поставка.
Описание: The solution of mixed boundary value problems requires considerable mathematical skills. These problems have applications to diverse fields, including fracture
mechanics, elasticity, plasticity, and biomechanics. "Mixed Boundary Value Problems" provides the skills necessary to solve these complex problems.
This book presents a
comprehensive treatment of integral equations and special functions. It demonstrates techniques such as separation of variables, transform methods, and conformal mapping, and
includes MATLAB[registered] to help with problem solving. The book also contains numerous illustrative problems for readers who wish to master the material in more depth.
Описание: The purpose of this book is to provide a careful and accessible account along modern lines of the subject which the title deals, as well as to discuss problems of current interest in the field. More precisely this book is devoted to the functional-analytic approach to a class of degenerate boundary value problems for second-order elliptic integro-differential operators which includes as particular cases the Dirichlet and Robin problems. This class of boundary value problems provides a new example of analytic semigroups. As an application, we construct a strong Markov process corresponding to such a diffusion phenomenon that a Markovian particle moves both by jumps and continuously in the state space until it dies at the time when it reaches the set where the particle is definitely absorbed.
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: 7662 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.
Описание: The book is devoted to the topological fixed point theory both for single-valued and multivalued mappings in locally convex spaces, including its application to boundary value problems for ordinary differential equations (inclusions) and to (multivalued) dynamical systems. It is the first monograph dealing with the topological fixed point theory in non-metric spaces. Although the theoretical material was tendentiously selected with respect to applications, the text is self-contained. Therefore, three appendices concerning almost-periodic and derivo-periodic single-valued (multivalued) functions and (multivalued) fractals are supplied to the main three chapters. In Chapter I, the topological and analytical background is built. Then, in Chapter II, topological principles necessary for applications are developed. Finally, in Chapter III, boundary value problems for differential equations and inclusions are investigated in detail by means of the results in Chapter II. This monograph will be especially useful for post-graduade students and researchers interested in topological methods in nonlinear analysis, particularly in differential equations, differential inclusions and (multivalued) dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.
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.
ООО "Логосфера " Тел:+7(495) 980-12-10 www.logobook.ru