Kategoria BISAC: Mathematics >> Differential Equations - General

This book is about numerical modeling of multiscale problems, and introduces several asymptotic analysis and numerical techniques which are necessary for a proper approximation of equations that depend on different physical scales. Aimed at advanced undergraduate and graduate students in mathematics, engineering and physics or researchers seeking a no-nonsense approach, it discusses examples in their simplest possible settings, removing mathematical hurdles that might hinder a clear understanding of the methods.

The problems considered are given by singular perturbed reaction...

This book discusses the complex theory of differential equations or more precisely, the theory of differential equations on complex-analytic manifolds.

Although the theory of differential equations on real manifolds is well known it is described in thousands of papers and its usefulness requires no comments or explanations to date specialists on differential equations have not focused on the complex theory of partial differential equations. However, as well as being remarkably beautiful, this theory can be used to solve a number of problems in real theory, for instance, the Poincare...

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. Phase Transitions has been an active multidisciplinary field of research, bringing together physicists, computer scientists and mathematicians. The main research theme explores how atomic agents that act locally and microscopically lead to discontinuous macroscopic changes. Adopting this perspective has proven to be especially useful in studying the evolution of random and...

Sowohl im Studium als auch in der taglichen Arbeit benotigt der Physiker eine Vielzahl mathematischer Methoden, die uber die Methoden aus den Grundvorlesungen der Analysis und linearen Algebra hinausgehen. Das vorliegende Buch baut auf diesen Vorlesungen auf und stellt die grundlegenden und jeweils einfuhrenden Themen aus der Funktionentheorie, der Funktionalanalysis, der Theorie orthogonaler Polynome und Funktionen, der Fouriertheorie, der Tensorrechnung und der Distributionen dar. Bei der sehr kompakten Darstellung des Stoffes wurde darauf geachtet eine einheitliche und gebrauchliche...

Collating different aspects of Vector-valued Partial Differential Equations and Applications, this volume is based on the 2013 CIME Course with the same name which took place at Cetraro, Italy, under the scientific direction of John Ball and Paolo Marcellini. It contains the following contributions: The pullback equation (Bernard Dacorogna), The stability of the isoperimetric inequality (Nicola Fusco), Mathematical problems in thin elastic sheets: scaling limits, packing, crumpling and singularities (Stefan Muller), and Aspects of PDEs related to fluid...

This volume contains extended abstracts outlining selected talks and other selected presentations given by participants throughout the -Intensive Research Program on Advances in Nonsmooth Dynamics 2016-, held at the Centre de Recerca Matematica (CRM) in Barcelona from February 1st to April 29th, 2016. They include brief research articles reporting new results, descriptions of preliminary work or open problems, and outlines of prominent discussion sessions. The articles are all the result of direct collaborations initiated during the research program.

The topic is the theory and...

There are several physico-chemical processes that determine the behavior of multiphase fluid systems - e.g., the fluid dynamics in the different phases and the dynamics of the interface(s), mass transport between the fluids, adsorption effects at the interface, and transport of surfactants on the interface - and result in heterogeneous interface properties. In general, these processes are strongly coupled and local properties of the interface play a crucial role. A thorough understanding of the behavior of such complex flow problems must be based on physically sound mathematical models,...