Hasil Pencarian  ::  Simpan CSV :: Kembali

"This monograph explores nonoscillation and existence of positive solutions for functional differential equations and describes their applications to maximum principles, boundary value problems and stability of these equations. In view of this objective the volume considers a wide class of equations including, scalar equations and systems of different types, equations with variable types of delays and equations with variable deviations of the argument. Each chapter includes an introduction and preliminaries, thus making it complete. Appendices at the end of the book cover reference material."

"This book offers on the one hand a complete theory of Sobolev spaces, which are of fundamental importance for elliptic linear and non-linear differential equations, and explains on the other hand how the abstract methods of convex analysis can be combined with this theory to produce existence results for the solutions of non-linear elliptic boundary problems. The book also considers other kinds of functional spaces which are useful for treating variational problems such as the minimal surface problem."

"A unified discussion of the formulation and analysis of special methods of mixed initial boundary-value problems. The focus is on the development of a new mathematical theory that explains why and how well spectral methods work. Included are interesting extensions of the classical numerical analysis."

"Solutions of the wave equation or Maxwell's equations in boundary value and free space problems are analyzed. Hyperbolic systems in domains going off to infinity are studied. New results on Maxwell's equations and non-star shaped reflecting bodies are included."

"The soliton is a dramatic concept in nonlinear science. What makes this book unique in the treatment of this subject is its focus on the properties that make the soliton physically ubiquitous and the soliton equation mathematically miraculous. Here, on the classical level, is the entity field theorists have been postulating for years: a local traveling wave pulse; a lump-like coherent structure; the solution of a field equation with remarkable stability and particle-like properties. It is a fundamental mode of propagation in gravity- driven surface and internal waves; in atmospheric waves; in ion acoustic and Langmuir waves in plasmas; in some laser waves in nonlinear media; and in many biologic contexts, such as alpha- helix proteins. This is not an encyclopedia of information on solitons in which every sentence is interrupted by either a caveat or a reference. Rather, Newell has tried to tell the story of the soliton as he would have liked to have heard it as a graduate student, with some historical development, lots of motivation, and frequent attempts to relate the topic at hand to the big picture. The book begins with a history of the soliton from its first sighting to the discovery of the inverse scattering method and recent ideas on the algebraic structure of soliton equations. Chapter 2 focuses on the universal nature of these equations and how and why they arise in physical and engineering contexts as asymptotic solvability conditions. The third chapter deals with the inverse scattering method and perturbation theories. Chapter 4 introduces the t-function and discusses the relations between the various methods for constructing solutions to the soliton equations and their various properties. Finally, an algebraic structure for the equations is provided in Chapter 5."

"In order to emphasize the relationships and cohesion between analytical and numerical techniques, Ordinary Differential Equations in Theory and Practice presents a comprehensive and integrated treatment of both aspects in combination with the modeling of relevant problem classes. This text is uniquely geared to provide enough insight into qualitative aspects of ordinary differential equations (ODEs) to offer a thorough account of quantitative methods for approximating solutions numerically, and to acquaint the reader with mathematical modeling, where such ODEs often play a significant role.Although originally published in 1995, the text remains timely and useful to a wide audience. It provides a thorough introduction to ODEs, since it treats not only standard aspects such as existence, uniqueness, stability, one-step methods, multistep methods, and singular perturbations, but also chaotic systems, differential-algebraic systems, and boundary value problems. The authors aim to show the use of ODEs in real life problems, so there is an extended chapter in which not only the general concepts of mathematical modeling but also illustrative examples from various fields are presented. A chapter on classical mechanics makes the book self-contained."