Kategoria BISAC: Mathematics >> Differential Equations - General

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...

This book provides a self-contained introduction to the theory of infinite-dimensional systems theory and its applications to port-Hamiltonian systems. The textbook starts with elementary known results, thenprogresses smoothly to advanced topics in current research.

Many physical systems can be formulated using a Hamiltonian framework, leading to models described by ordinary or partial differential equations. For the purpose of control and for the interconnection of two or more Hamiltonian systems it is essential to take into account this interaction with the environment. This book...

This monograph fits theclearlyneed for books with a rigorous treatment of theinverse problems for non-classical systems and that of initial-boundary-value problems for integrable nonlinear equations. The authorsdevelop a unified treatment of explicit and global solutions via the transfer matrix function in a form due to Lev A. Sakhnovich.

The book primarily addresses specialists in the field. However, it is self-contained andstarts with preliminaries and examples, and hencealso serves as an introduction for advanced graduate students in the field.

This fourth issue on "progress in turbulence" is based on the fourth ITI conference (ITI interdisciplinary turbulence initiative), which took place in Bertinoro, North Italy. Leading researchers from the engineering and physical sciences presented latest results in turbulence research. Basic as well as applied research is driven by the rather notorious difficult and essentially unsolved problem of turbulence. In this collection of contributions clear progress can be seen in different aspects, ranging from new quality of numerical simulations to new concepts of experimental investigations...

This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations. It presents the necessary material on Fourier transformation and distribution theory, the basic calculus of pseudodifferential operators on the n-dimensional Euclidean space, an introduction to the theory of singular integral operators, the modern theory of Besov and Bessel potential spaces, and several applications to wellposedness and regularity question for elliptic and parabolic equations. The basic notation...

The book collects the most significant contributions of the outstanding Czech mathematician Jindřich Nečas, who was honoured with the Order of Merit of the Czech Republic by President Vaclav Havel. Starting with Nečas's brief biography and short comments on his role in the beginnings of modern PDE research in Prague, the book then follows the periods of his research career. The first part is devoted to the linear theory of partial differential equations. Its topics include the variational approach to linear boundary value problems and the Rellich - Nečas inequalities,...

Inequalities arise as an essential component in various mathematical areas. Besides forming a highly important collection of tools, e.g. for proving analytic or stochastic theorems or for deriving error estimates in numerical mathematics, they constitute a challenging research field of their own. Inequalities also appear directly in mathematical models for applications in science, engineering, and economics.

This edited volume covers divers aspects of this fascinating field. It addresses classical inequalities related to means or to convexity as well as inequalities arising...

"Hypernumbers and Extrafunctions" presents a rigorous mathematical approach to operate with infinite values. First, concepts of real and complex numbers are expanded to include a new universe of numbers called hypernumbers which includes infinite quantities. This brief extends classical calculus based on real functions by introducing extrafunctions, which generalize not only the concept of a conventional function but also the concept of a distribution. Extrafucntions have been also efficiently used for a rigorous mathematical definition of the Feynman path integral, as well as for...

Recent Advances in Harmonic Analysis and Applications features selected contributions from the AMS conference which took place at Georgia Southern University, Statesboro in 2011 in honor of Professor Konstantin Oskolkov's 65th birthday. The contributions are based on two special sessions, namely "Harmonic Analysis and Applications" and "Sparse Data Representations and Applications." Topics covered range from Banach space geometry to classical harmonic analysis and partial differential equations. Survey and expository articles by leading experts in their corresponding fields are...