Bøger i Monographs and Surveys in Pure and Applied Mathematics serien

This monograph is designed to act as a companion volume to more advanced texts by gathering together the principal mathematical topics commonly used in developing scattering theories and, in so doing, provide a reasonable self-contained introduction to linear and nonlinear scattering theory.

This, and a companion volume, provides an account of complex analytic methods for partial differential equations and their applications. The authors focus on applications in acoustics, fluid dynamics and wave motion.

Examines periodic solutions of impulsive differential equations. Periodic linear impulsive differential equations, the use of the small parameter method in noncritical and critical cases, and the existence of periodic solutions of nonlinear differential equations are discussed.

Although the theory behind solitary waves of strain shows that they hold promise in nondestructive testing and a variety of other applications, an enigma has long persisted-the absence of observable solitary waves in practice. Inspired by this contradiction, Strain Solitons in Solids and How to Construct Them refines the theory, explores how to con

Geometric ideas and techniques play an important role in operator theory and the theory of operator algebras. This title builds the background to understand this circle of ideas and reports on developments in this field of research. It introduces infinite dimensional Lie theory, emphasising on the relationship between Lie groups and Lie algebras.

Presents the ray method for studying nonlinear wave propagation in fluid dynamics and plasma physics. Topics covered are shock wave propagation, the derivation of model equations in several dimensions (dissipative and dispersive) and the interaction of waves, both hyperbolic and dispersive.

Part of the "Pitman Monographs in Pure and Applied Mathematics" series, this text presents various problems of partial differential equations. It covers elliptic systems degenerated at the boundary, overdetermined boundary value problems and initial boundary value problems.

Focuses on the principal spectral theory for general time-dependent and random parabolic equations and systems. This book addresses Faber-Krahn inequalities for elliptic and time-periodic problems and extends the linear theory for scalar nonautonomous and random parabolic equations to cooperative systems.

Hamiltonian fluid dynamics and stability theory work hand-in-hand in a variety of engineering, physics, and physical science fields. Until now, however, no single reference addressed and provided background in both of these closely linked subjects. Introduction to Hamiltonian Fluid Dynamics and Stability Theory does just that-offers a comprehensive introduction to Hamiltonian fluid dynamics and describes aspects of hydrodynamic stability theory within the context of the Hamiltonian formalism.The author uses the example of the nonlinear pendulum-giving a thorough linear and nonlinear stability analysis of its equilibrium solutions-to introduce many of the ideas associated with the mathematical argument required in infinite dimensional Hamiltonian theory needed for fluid mechanics. He examines Andrews'' Theorem, derives and develops the Charney-Hasegawa-Mima (CMH) equation, presents an account of the Hamiltonian structure of the Korteweg-de Vries (KdV) equation, and discusses the stability theory associated with the KdV soliton.The book''s tutorial approach and plentiful exercises combine with its thorough presentations of both subjects to make Introduction to Hamiltonian Fluid Dynamics and Stability Theory an ideal reference, self-study text, and upper level course book.

In recent years, progress in the field of SCQM (supersymmetric classical and quantum mechanics) has been dramatic and the literature continues to grow. This monograph offers an overview of the field and summarizes the major developments of the last 15 years. It provides both a review of the literature and a detailed exposition of the underlying SCQM principles. For those just beginning in the field, the author presents step-by-step details of most of the computations. For more experienced readers, the treatment includes systematic analyses of more advanced topics, such as quasi- and conditional solvability and the role of supersymmetry in nonlinear systems.

This Research Note sets forth a comprehensive description of various aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. The authors present the material in the context of the important applications of such systems, including the Euler equations of gas dynamics, magnetohydrodynamics , shallow water, and solid dynamics equations. This work systematizes methods for overcoming the difficulties inherent in the solution of hyperbolic systems. Its unique focus on applications, both traditional and new, makes it valuable not only to those interested the development of numerical methods, but also to physicists and engineers.

Relevant to a variety of mathematical models in physics, engineering, and finance, this volume studies Cauchy problems that are not well-posed in the classical sense. It brings together and examines three major approaches to treating such problems: semigroup methods, abstract distribution methods, and regularization methods. Although extensively developed over the last decade, the authors provide a unique, self-contained account of these methods and demonstrate the profound connections between them. Accessible to beginning graduate students, this volume brings together many different ideas to serve as a reference on modern methods for abstract linear evolution equations.

Inverse boundary problems are a rapidly developing area of applied mathematics. Inverse boundary spectral problems (IBSP) constitute an important and distinct part of the field because of the special character of the data involved, the specific methods used to deal with that data, and their relevance to applications, including medical imaging and geophysical prospecting. Although the theory of ISBP has been in development for at least 10 years, this book was published, the literature had been scattered throughout various journals. This self-contained monograph summarizes IBSP concepts and the techniques useful for dealing with them.

Interfacial Phenomena and Convection is a self-contained monograph that examines a rich variety of phenomena in which interfaces play a crucial role. From a unified perspective that embraces physical chemistry, fluid mechanics, and applied mathematics, the authors study recent developments related to the Marangoni effect, including patterned convection and instabilities, oscillatory/wavy phenomena, and turbulent phenomena. They examine Bénard layers subjected to transverse and longitudinal thermal gradients and phenomena involving surface tension gradients as the driving forces, including falling films, drops, and liquid bridges.

Models for the mechanical behavior of porous media introduced more than 50 years ago are still relied upon today, but more recent work shows that they may sometimes violate the laws of thermodynamics. This monograph shows that physical consistency requires a unique description of dynamic processes that involve porous media and that new dynamic variables naturally enter into the large-scale description of porous media. The implications of the physical theory presented in this book are significant, particularly in applications in geophysics and the petroleum industry. The Thermophysics of Porous Media offers a unique opportunity to examine the dynamic role that porosity plays in porous materials.

The interest of these authors lies in explicit, canonical-form characterizations of isometries on Banach spaces, and in this monograph, they explore the topic in the context of classical function spaces. Designed for both experts and beginners in the field, their treatment presents a history of the subject, the important results, and a look at some of the wide variety of methods used in addressing the characterization problem in various types of spaces. The authors faithfully report the results of other researchers' original papers and offer some enlightening clarifications. Each chapter is self-contained and includes notes and remarks that touch upon related results and other approaches not addressed in the main text.

This book offers a systematic presentation of the modern theory of the stability of stochastic differential equations in infinite dimensional spaces - particularly Hilbert spaces. The treatment includes a review of basic concepts and investigation of the stability theory of linear and nonlinear stochastic differential equations and stochastic functional differential equations in infinite dimensions. The final chapter explores topics and applications such as stochastic optimal control and feedback stabilization, stochastic reaction-diffusion, Navier-Stokes equations, and stochastic population dynamics. This book makes up-to-date material accessible and lays the foundation for future advances.

This book presents a systematic, detailed development of approaches to construct ¿ uniformly convergent finite difference schemes for wide classes of singularly perturbed boundary value problems. The first part of the book explores boundary value problems for elliptic and parabolic reaction-diffusion and convection-diffusion equations in n-dimensional domains with smooth and piecewise-smooth boundaries. Containing material published mainly in the last four years, the second section focuses on problems with boundary layers and additional singularities generated by nonsmooth data, unboundedness of the domain, and the perturbation vector parameter.

Since higher order derivatives are useful in many places, nth order derivatives are often defined directly. These derivatives are more general than the ordinary derivative and are useful in many purposes. This book discusses higher order derivatives and the relations among them. It covers higher order generalized derivatives, including Peano derivative, d.l.V.P. derivative, symmetric and unsymmetric Riemann derivative, symmetric and unsymmetric Cesàro derivative, symmetric and unsymmetric Borel derivative, symmetric and unsymmetric LP-derivative, symmetric and unsymmetric Laplace derivative, and Abel derivative.

Studies Cauchy problems that are not well-posed in the classical sense. This volume presents and examines three major approaches to treating such problems: semigroup methods, abstract distribution methods, and regularization methods.

Details the construction of a Lorentz invariant thermodynamic lattice gas model and shows how the associated nonrelativistic, Galilean invariant model can be used to describe flow in porous media. This work develops the equations of seismic wave propagation in porous media, the associated boundary conditions, and surface waves.

Surveys investigations of Banach-space isometries. This volume emphasizes the characterization of isometries and focuses on establishing the type of explicit, canonical form in a variety of settings. It describes the isometries on classical function spaces. It explores isometries on Banach algebras.

The computational power available means that practitioners can find accurate approximations to the solutions of more sophisticated mathematical models. This book describes a class of techniques that fulfill this need by providing closed-form solutions to many boundary value problems that arise in science and engineering.

Presents a comprehensive description of various aspects of problems originating in numerical solution of hyperbolic systems of partial differential equations. This work systematizes methods for overcoming the difficulties inherent in the solution of hyperbolic systems. It is suitable for those interested in the development of numerical methods.

This text presents a theory of generalized Cauchy-Riemann systems with the order of the polar singularities not less than one and discusses its application to the study of infinitesimal bendings of positive curvature surfaces with an isolated flat point.

This text deals with the two-dimensional Riemann problem for Euler equations in gas dynamics and its mathematical simplification. For Euler equations it is classified into 18 cases according to the different combinations of four elementary plane waves emanated by initial discontinuities.

This study of regular differential operators covers topics such as linear and banach spaces, interpolation of spaces and operators, unbounded polynomial operator pencils, n-fold completeness of root vectors of an unbounded polynomial operator pencil and p-regular functional conditions.

Part of the "Pitman Monographs and Surveys in Pure and Applied Mathematics" series, this text examines mathematical problems of classical nonlinear electromagnetic theory.