General

This volume collects six articles on selected topics at the frontier between partial differential equations and spectral theory, written by leading specialists in their respective field. The articles focus on topics that are in the center of attention of...

Gunter Lumer was an outstanding mathematician whose work has great influence on the research community in mathematical analysis and evolution equations. He was at the origin of the breath-taking development the theory of semigroups saw after the...

Complex, microstructured materials are widely used in industry and technology and include alloys, ceramics and composites. Focusing on non-destructive evaluation (NDE), this book explores in detail the mathematical modeling and inverse problems...

This work provides a detailed and up-to-the-minute survey of the various stability problems that can affect suspension bridges. In order to deduce some experimental data and rules on the behavior of suspension bridges, a number of historical events are...

The aim of this volume that presents lectures given at a joint CIME and Banach Center Summer School, is to offer a broad presentation of a class of updated methods providing a mathematical framework for the development of a hierarchy of models of complex...

This book aims to establish a foundation for fractional derivatives and fractional differential equations. The theory of fractional derivatives enables considering any positive order of differentiation. The history of research in this field is very long,...

This book is intended for students of computational systems biology with only a limited background in mathematics. Typical books on systems biology merely mention algorithmic approaches, but without offering a deeper understanding. On the other hand,...

The Euler and Navier-Stokes equations are the fundamental mathematical models of fluid mechanics, and their study remains central in the modern theory of partial differential equations. This volume of articles, derived from the workshop 'PDEs in Fluid...

This volume contains the proceedings of talks presented at the 11th International Conference on Difference Equations and Applications (ICDEA 2006). It will be titled "International conference on Advances in discrete dynamical systems". ICDEA 2006 was...

This book collects papers presented during the European Workshop on High Order Nonlinear Numerical Methods for Evolutionary PDEs (HONOM 2013) that was held at INRIA Bordeaux Sud-Ouest, Talence, France in March, 2013. The central topic is high order...

Topics in Fractional Differential Equations is devoted to the existence and uniqueness of solutions for various classes of Darboux problems for hyperbolic differential equations or inclusions involving the Caputo fractional derivative. Fractional...

Many phenomena of interest for applications are represented by differential equations which are defined in a domain whose boundary is a priori unknown, and is accordingly named a "free boundary". A further quantitative condition is then...

This engaging text describes the development of singular perturbations, including its history, accumulating literature, and its current status. While the approach of the text is sophisticated, the literature is accessible to a broad audience. A...

This book details the mathematical developments in total variation based image restauration. From the reviews: "This book is devoted to PDE's of elliptic and parabolic type associated to functionals having a linear growth in the gradient, with a...

Necas' book Direct Methods in the Theory of Elliptic Equations, published 1967 in French, has become a standard reference for the mathematical theory of linear elliptic equations and systems. This English edition, translated by G. Tronel and A. Kufner,...

Beginning with the works of N.N.Krasovskii [81, 82, 83], which clari fied the functional nature of systems with delays, the functional approach provides a foundation for a complete theory of differential equations with delays. Based on the functional...

This book presents mathematical models that arise in current photographic science. The book contains seventeen chapters, each dealing with one area of photographic science, and a final chapter containing exercises. Each chapter, except the two...

Interfaces are geometrical objects modelling free or moving boundaries and arise in a wide range of phase change problems in physical and biological sciences, particularly in material technology and in dynamics of patterns. Especially in the end of last...

Optimization problems subject to constraints governed by partial differential equations (PDEs) are among the most challenging problems in the context of industrial, economical and medical applications. Almost the entire range of problems in this field of...

This book introduces the reader to solving partial differential equations (PDEs) numerically using element-based Galerkin methods. Although it draws on a solid theoretical foundation (e.g. the theory of interpolation, numerical integration, and function...

This volume contains extended abstracts outlining selected presentations given by participants of the joint international multidisciplinary workshop MURPHYS-HSFS-2016 (MUltiRate Processes and HYSteresis; Hysteresis and Slow-Fast Systems), which was...

Differential equations with delay naturally arise in various applications, such as control systems, viscoelasticity, mechanics, nuclear reactors, distributed networks, heat flows, neural networks, combustion, interaction of species, microbiology,...

This book is comprehensive in its classical mathematical physics presentation, providing the reader with detailed instructions for obtaining Green's functions from scratch. Green's functions is an instrument easily accessible to practitioners who are...

This work collects the most important results presented at the Congress on Differential Equations and Applications/Congress on Applied Mathematics (CEDYA/CMA) in Cadiz (Spain) in 2015. It supports further research in differential equations, numerical...

This book focuses on Hamilton's Ricci flow, beginning with a detailed discussion of the required aspects of differential geometry, progressing through existence and regularity theory, compactness theorems for Riemannian manifolds, and Perelman's...

Containing the proceedings from the 41st conference on Boundary Elements and other Mesh Reduction Methods (BEM/MRM), this book is a collection of high quality papers that report on advances in techniques that reduce or eliminate the type of meshes...

This book provides a unified analysis and scheme for the existence and uniqueness of strong and mild solutions to certain fractional kinetic equations. This class of equations is characterized by the presence of a nonlinear time-dependent source,...

Because the theory of equations with delay terms occurs in a variety of contexts, it is important to provide a framework, whenever possible, to handle as many cases as possible simultaneously so as to bring out a better insight and understanding of the...

This monograph presents a rigorous mathematical framework for a linear elastic model arising from volcanology that explains deformation effects generated by inflating or deflating magma chambers in the Earth's interior. From a mathematical perspective,...

This book is an outcome of two Conferences on Ulam Type Stability (CUTS) organized in 2016 (July 4-9, Cluj-Napoca, Romania) and in 2018 (October 8-13, 2018, Timisoara, Romania). It presents up-to-date insightful perspective and very resent research...

'Et moi, ..., si j'avait su comment en reveru.r, One service mathematics has rendered the je n'y scrais point aIle.' human race. It has put common sense back Jules Verne where it belongs, on the topmost shelf next to the dusty canister labelled...

Boundary value problems for partial differential equations playa crucial role in many areas of physics and the applied sciences. Interesting phenomena are often connected with geometric singularities, for instance, in mechanics. Elliptic operators in...

This two-volume textbook provides comprehensive coverage of partial differential equations, spanning elliptic, parabolic, and hyperbolic types in two and several variables. In this first volume, special emphasis is placed on geometric and complex...

This advanced book focuses on ordinary differential equations (ODEs) in Banach and more general locally convex spaces, most notably the ODEs on measures and various function spaces. It briefly discusses the fundamentals before moving on to the cutting...

This book presents the various algebraic techniques for solving partial differential equations to yield exact solutions, techniques developed by the author in recent years and with emphasis on physical equations such as: the Maxwell equations, the Dirac...

This book features a collection of recent findings in Applied Real and Complex Analysis that were presented at the 3rd International Conference "Boundary Value Problems, Functional Equations and Applications" (BAF-3), held in Rzeszow, Poland on 20-23...

A comprehensive description of the current theoretical and numerical aspects of inverse problems in partial differential equations. Applications include recovery of inclusions from anomalies of their gravity fields, reconstruction of the interior of the...

Preface Constructing nonlinear parameter-dependent mathematical models is essential in modeling in many scientific research fields. The investigation of branching (bifurcating) solutions of such equations is one of the most important aspects in the...

The book includes lectures given by the plenary and key speakers at the 9th International ISAAC Congress held 2013 in Krakow, Poland. The contributions treat recent developments in analysis and surrounding areas, concerning topics from the theory of...

The geometrical theory of nonlinear differential equations originates from classical works by S. Lie and A. Backlund. It obtained a new impulse in the sixties when the complete integrability of the Korteweg-de Vries equation was found and it became...