Bücher der Reihe Applied Mathematical Sciences

Filling the gap between the mathematical literature and applications to domains, the authors have chosen to address the problem of wave collapse by several methods ranging from rigorous mathematical analysis to formal aymptotic expansions and numerical simulations.

This marks the 100th volume to appear in the Applied Mathematical Sci ences series. One year prior to its appearance, the then mathematics editor of Springer-Verlag, Klaus Peters, organized a meeting to look into the possibility of starting a series slanted toward applications.

Our text, based on the old notes and experience gained in many courses, seminars, and conferences, both in Italy and abroad, aims to give a simple and rapid introduction to the various themes, problems, and methods of the theory of ordinary differential equations.

The theoretical part of the work is developed in Chapters 2-14, while in Chapters 15-19 we apply the theory to several remarkable partial differ ential equations.

Presents the description of the state of the modern iterative techniques together with systematic analysis. This book discusses classical methods, semi-iterative techniques, incomplete decompositions, conjugate gradient methods, multigrid methods and domain decomposition techniques.

Of interest to everybody working on perturbation theory in differential equations, this book requires only a standard mathematical background in engineering and does not require reference to the special literature. systems of ordinary differential equations with small parameters; reconstruction and equations in partial derivatives.

This book introduces mathematical techniques needed to analyse PDEs coming from incompressible fluid mechanics, including Stokes and Navier-Stokes equations and more specific models, and offering methods applicable to a range of domains in nonlinear analysis.

This book summarizes effective and general approaches and frameworks in the investigation of bifurcation phenomena for functional differential equations (FDEs). It provides all the tools from bifurcation theory and contains examples and applications.

Brownian dynamics play a key role in molecular and cellular biophysics. This book is aimed at applied mathematicians, physicists, theoretical chemists and physiologists interested in the modeling, analysis and simulation of micro devices of microbiology.

It had its origin in a project initiated jointly with the IBM Cambridge Scien tific Center, particularly with Dr. Rhett Tsao, then of that Center. Professors Donald McClure and Richard Vitale of the Division of Applied Mathematics at Brown University contributed greatly to the project and taught courses in its spirit.

This book deals with optimality conditions, algorithms, and discretization tech niques for nonlinear programming, semi-infinite optimization, and optimal con trol problems.

Chapter 9 is a new chapter on perturbed systems. The remainder of the material has been completely revised and updated with the most significant changes occurring in Chapter 3 on the properties of solutions, Chapter 5 on stability, and Chapter lOon behavior near a periodic orbit.

In the summer of 1941 Brown University undertook a Program of Advanced Instruction and Research in Mechanics. Indeed in certain instances only in the last few years has the -field caught up with the ideas developed in the course of these lectures.

Focusing on large-amplitude patterns far from equilibrium in biologically relevant models, this book summarizes and expands on fifteen years of results in the mathematical analysis of patterns which are encountered in biological systems.

This book, now in its third edition, is an excellent introductory text for students, scientists and engineers who want to learn the basic theory of linear integral equations and their numerical solution. Features problems at the end of each chapter.

This book gives a concise introduction to the basic techniques needed for the theoretical analysis of the Maxwell Equations, and filters in an elegant way the essential parts, e.g., concerning the various function spaces needed to rigorously investigate the boundary integral equations and variational equations.

This book is about two special topics in rheological fluid mechanics: the elasticity of liquids and asymptotic theories of constitutive models.

This book provides an introduction to dynamical systems with multiple time scales. The target audience of this book are senior undergraduates, graduate students as well as researchers interested in using the multiple time scale dynamics theory in nonlinear science, either from a theoretical or a mathematical modeling perspective.

The Nonlinear Schrodinger Equation

This book covers numerical methods for stochastic partial differential equations with white noise using the framework of Wong-Zakai approximation. In addition, stochastic Euler equations are exploited as an application of stochastic collocation methods, where a numerical comparison with other integration methods in random space is made.

Allows the reader to explore nonlinear dynamics and chaos by the use of illustrated graphics. This title is suitable for research and educational needs.

Selected applications are accompanied by numerical simulations illustrating both the models and the efficiency of computational algorithms. In this book, the mathematical framework for a rigorous mathematical treatment of "rate-independent systems" is presented in a comprehensive form for the first time.

By presenting the data in a readable and informative manner, the book introduces both scientific and engineering researchers as well as graduate students to the significant work done in this area in recent years, relating it to broader themes in mathematical analysis.

The fourth and final part, Introduction to Partial Differential Equations, serves as an introduction to modern methods for classical theory of partial differential equations. Complete with nearly 250 exercises throughout, this text is intended for graduate level students and researchers in the mathematical sciences and engineering.

This book presents an in-depth treatment of various mathematical aspects of electromagnetism and Maxwell's equations: from modeling issues to well-posedness results and the coupled models of plasma physics (Vlasov-Maxwell and Vlasov-Poisson systems) and magnetohydrodynamics (MHD).

Singular perturbations occur when a small coefficient affects the highest order derivatives in a system of partial differential equations. From the physical point of view singular perturbations generate in the system under consideration thin layers located often but not always at the boundary of the domains that are called boundary layers or internal layers if the layer is located inside the domain. Important physical phenomena occur in boundary layers. The most common boundary layers appear in fluid mechanics, e.g., the flow of air around an airfoil or a whole airplane, or the flow of air around a car. Also in many instances in geophysical fluid mechanics, like the interface of air and earth, or air and ocean. This self-contained monograph is devoted to the study of certain classes of singular perturbation problems mostly related to thermic, fluid mechanics and optics and where mostly elliptic or parabolic equations in a bounded domain are considered. This book is a fairly unique resource regarding the rigorous mathematical treatment of boundary layer problems. The explicit methodology developed in this book extends in many different directions the concept of correctors initially introduced by J. L. Lions, and in particular the lower- and higher-order error estimates of asymptotic expansions are obtained in the setting of functional analysis. The review of differential geometry and treatment of boundary layers in a curved domain is an additional strength of this book. In the context of fluid mechanics, the outstanding open problem of the vanishing viscosity limit of the Navier-Stokes equations is investigated in this book and solved for a number of particular, but physically relevant cases.This book will serve as a unique resource for those studying singular perturbations and boundary layer problems at the advanced graduate level in mathematics or applied mathematics and may be useful for practitioners in other related fields in science and engineering such as aerodynamics, fluid mechanics, geophysical fluid mechanics, acoustics and optics.

Shapes are complex objects to apprehend, as mathematical entities, in terms also suitable for computerized analysis and interpretation. This volume provides the background that is required for this purpose, including different approaches that can be used.

Several types of differential equations, such as functional differential equation, age-structured models, transport equations, reaction-diffusion equations, and partial differential equations with delay, can be formulated as abstract Cauchy problems with non-dense domain.