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Shape Optimization by the Homogenization Method
The topic of this book is homogenization theory and its applications to optimal design in the conductivity and elasticity settings. Its purpose is to give a self-contained account …
Theory and Applications of Stochastic Processes
Stochastic processes and diffusion theory are the mathematical underpinnings of many scientific disciplines, including statistical physics, physical chemistry, molecular …
Nonlinear Theory of Shallow Shells
This book presents rigorous treatment of boundary value problems in nonlinear theory of shallow shells. The consideration of the problems is carried out using methods of nonlinear …
Matched Asymptotic Expansions
Content and Aims of this Book Earlier drafts of the manuscript of this book (James A. Boa was then coau thor) contained discussions of many methods and examples of singular …
Mathematical Tools for the Study of the Incompressible Navier-Stokes Equations andRelated Models
The objective of this self-contained book is two-fold. First, the reader is introduced to the modelling and mathematical analysis used in fluid mechanics, especially concerning …
The Energy Method, Stability, and Nonlinear Convection
This book is a revised edition of my earlier book of the same title. The cur rent edition adopts the structure of the earlier version but is much changed. The introduction now …
Weakly Connected Neural Networks
This book is devoted to an analysis of general weakly connected neural networks (WCNNs) that can be written in the form (0.1) m Here, each Xi E IR is a vector that summarizes all …
Mathematical Problems in Image Processing
Partial differential equations (PDEs) and variational methods were introduced into image processing about fifteen years ago. Since then, intensive research has been carried out. …
Manifolds, Tensor Analysis, and Applications
The purpose of this book is to provide core material in nonlinear analysis for mathematicians, physicists, engineers, and mathematical biologists. The main goal is to provide a …
Numerical Quadrature and Solution of Ordinary Differential Equations
This is a textbook for a one semester course on numerical analysis for senior undergraduate or beginning graduate students with no previous knowledge of the subject. The …
Semidynamical Systems in Infinite Dimensional Spaces
Where do solutions go, and how do they behave en route? These are two of the major questions addressed by the qualita tive theory of differential equations. The purpose of this …
Perturbation Methods in Non-Linear Systems
This volume is intended to provide a comprehensive treatment of recent developments in methods of perturbation for nonlinear systems of ordinary differ ential equations. In this …