This is the first book to present a detailed discussion of both classical and recent results on the popular Cahn-Hilliard equation and some of its variants. The focus is on mathematical analysis of Cahn-Hilliard models, with an emphasis on thermodynamically relevant logarithmic nonlinear terms, for which several questions are still open. ......
This book provides an overview of the myriad methods for applying dynamical systems techniques to PDEs and highlights the impact of PDE methods on dynamical systems. Also included are many nonlinear evolution equations, which have been benchmark models across the sciences, and examples and techniques to strengthen preparation for research. PDE ......
Riemann-Hilbert problems are fundamental objects of study within complex analysis. Many problems in differential equations and integrable systems, probability and random matrix theory, and asymptotic analysis can be solved by reformulation as a Riemann-Hilbert problem. This book, the most comprehensive one to date on the applied and ......
Bose-Einstein condensation is a phase transition in which a fraction of particles of a boson gas condenses into the same quantum state known as the Bose-Einstein condensate (BEC). The aim of this book is to present a wide array of findings in the realm of BECs and on the nonlinear Schroedinger-type models that arise therein. The Defocusing ......
Concepts, Algorithms, and Applications to Chemical Processes
This book addresses modern nonlinear programming (NLP) concepts and algorithms, especially as they apply to challenging applications in chemical process engineering. The author provides a firm grounding in fundamental NLP properties and algorithms, and relates them to real-world problem classes in process optimization, thus making the material ......
An analysis of wave interactions for general systems of hyperbolic and viscous conservation laws. This self-contained study of shock waves explains the new wave phenomena from both a physical and a mathematical standpoint. The analysis should be useful for the study of various physical situations, including nonlinear elasticity, ......
Control of Nonlinear Systems to Achieve Performance Objectives
H* control originated in an effort to codify classical control methods where one shapes frequency response functions to meet certain objectives. H* control underwent tremendous development in the 1980s and made considerable strides toward systematizing classical control. This book addresses the next major issue - how this extends to nonlinear ......
