Differential calculus and equations

Fractional calculus is a rapidly growing field of research, at the interface between probability, differential equations, and mathematical physics.

The monograph is devoted to the study of initial-boundary-value problems for multi-dimensional Sobolev-type equations over bounded domains.

This is the first part of the second revised and extended edition of the well established book "e;Function Spaces"e; by Alois Kufner, Oldrich John, and Svatopluk Fucik.

This textbook provides a self-contained and elementary introduction to the modern theory of pseudodifferential operators and their applications to partial differential equations.

The intention of this textbook is to provide both, the theoretical and computational tools that are necessary to investigate and to solve optimal control problems with ordinary differential equations and differential-algebraic equations.

The theory of ill-posed problems originated in an unusual way.

The present collection is the very first contribution of this type in the field of sparse recovery.

This book is devoted to impulsive functional differential equations which are a natural generalization of impulsive ordinary differential equations (without delay) and of functional differential equations (without impulses).

This book is divided into two parts, the first of which seeks to connect the phase transitions of various disciplines, including game theory, and to explore the synergies between statistical physics and combinatorics.

The monograph is devoted to one of the most important trends in contemporary mathematical physics, the investigation of evolution equations of many-particle systems of statistical mechanics.

This book is a collection of state-of-the-art surveys on various topics in mathematical finance, with an emphasis on recent modelling and computational approaches.

This book deals with algorithms for the solution of linear systems of algebraic equations with large-scale sparse matrices, with a focus on problems that are obtained after discretization of partial differential equations using finite element methods.

This book presents the basic concepts and recent developments of linear control problems with perturbations.

Significant interest in the investigation of systems with discontinuous trajectories is explained by the development of equipment in which significant role is played by impulsive control systems and impulsive computing systems.

This text contains a series of self-contained reviews on the state of the art in different areas of partial differential equations, presented by French mathematicians.

This textbook presents a first introduction to PDEs on an elementary level, enabling the reader to understand what partial differential equations are, where they come from and how they can be solved.

The main classes of inverse problems for equations of mathematical physics and their numerical solution methods are considered in this book which is intended for graduate students and experts in applied mathematics, computational mathematics, and mathematical modelling.

The authors present functional analytical methods for solving a class of partial differential equations.

This monograph presents the state of the art of convexity, with an emphasis to integral representation.

This book deals with the reliable verification of the accuracy of approximate solutions which is one of the central problems in modern applied analysis.

Modeling, in particular with partial differential equations, plays an ever growing role in the applied sciences.

This book is the first comprehensive treatment of Painleve differential equations in the complex plane.

This book aims to establish a systematic theory on the synchronization for wave equations with locally distributed controls.

This book shows how Lie group and integrability techniques, originally developed for differential equations, have been adapted to the case of difference equations.

This book contains the historical development of the seminal paper of Adolf Hurwitz, professor in mathematics at ETH (1892~1919), and its impact on other fields.

Probabilistic methods can be applied very successfully to a number of asymptotic problems for second-order linear and non-linear partial differential equations.

This book is devoted to the relation between two different concepts of integrability: the complete integrability of complex analytical Hamiltonian systems and the integrability of complex analytical linear differential equations.

Das Skript ist für Studierende der Naturwissenschaften gedacht, die eine einführende Mathematikvorlesung besuchen.

This volume contains the Proceedings of the International Workshop Variational Methods For Discontinuous Structures, which was jointly organized by the Dipar- timento di Matematica Francesco Brioschi of Milano Politecnico and the Interna- tional School for Advanced Studies (SISSA) of Trieste.

Partial differential equations constitute an integral part of mathematics.

Many physical problems are meaningfully formulated in a cylindrical domain.

This set of lecture notes was written for a Nachdiplom-Vorlesungen course given at the Forschungsinstitut fUr Mathematik (FIM), ETH Zurich, during the Fall Semester 2000.

Multivariate polynomials are a main tool in approximation.

This volume contains research articles from the field of Nonlinear Differential Equa- tions which result from the "e;Workshop on Nonlinear Analysis and Applications"e; held in Bergamo on July 9 to 13, 200l.

The seventh International Conference on Evolution Equations and their main areas of Applications (where the emphasis evolves as time and problems change) was held October 30 to November 4 at the CIRM (Centro Internazionale per la Ricerca Matematica) in Trento, Italy.

The aim of the book is to present the state of the art of the theory of symmetric (Hermitian) matrix Riccati equations and to contribute to the development of the theory of non-symmetric Riccati equations as well as to certain classes of coupled and generalized Riccati equations occurring in differential games and stochastic control.

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In November 2001 the Mathematical Research Center at Oberwolfach, Germany, hosted the third Conference on Mathematical Models and Numerical Simulation in Electronic Industry.

The goal of this book is to present some modern aspects of nonlinear analysis.