Kategoria BISAC: Mathematics >> Differential Equations - General

This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in B dlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related...

This book is devoted to the analysis of the basic boundary value problems for the Laplace equation in singularly perturbed domains.  The main purpose is to illustrate a method called Functional Analytic Approach, to describe the dependence of the solutions upon a singular perturbation parameter in terms of analytic functions. Here the focus is on domains with small holes and the perturbation parameter is the size of the holes. The book is the first introduction to the topic and covers the theoretical material and its applications to a series of problems that range from simple...

This book presents the latest developments in the theory of gradient flows in random walk spaces. A broad framework is established for a wide variety of partial differential equations on nonlocal models and weighted graphs. Within this framework, specific gradient flows that are studied include the heat flow, the total variational flow, and evolution problems of Leray-Lions type with different types of boundary conditions. With many timely applications, this book will serve as an invaluable addition to the literature in this active area of research.

Variational and Diffusion...

This book provides a successful solution to one of the central problems of mathematical fluid mechanics: the Leray’s problem on existence of a solution to the boundary value problem for the stationary Navier—Stokes system in bounded domains under sole condition of zero total flux. This marks the culmination of the authors' work over the past few years on this under-explored topic within the study of the Navier—Stokes equations. This book will be the first major work on the Navier—Stokes equations to explore Leray’s problem in detail. The results are presented with detailed...

This book covers a highly relevant and timely topic that is of wide interest, especially in finance, engineering and computational biology. The introductory material on simulation and stochastic differential equation is very accessible and will prove popular with many readers. While there are several recent texts available that cover stochastic differential equations, the concentration here on inference makes this book stand out. No other direct competitors are known to date. With an emphasis on the practical implementation of the simulation and estimation methods presented, the text will...