Measure-Valued Solutions for Nonlinear Evolution Equations on Banach Spaces and Their Optimal Control

This book offers the first comprehensive presentation of measure-valued solutions for nonlinear deterministic and stochastic evolution equations on infinite dimensional Banach spaces. Unlike traditional solutions, measure-valued solutions allow for a much broader class of abstract evolution equations to be addressed, providing a broader approach.
The book presents extensive results on the existence of measure-valued solutions for differential equations that have no solutions in the usual sense. It covers a range of topics, including evolution equations with continuous/discontinuous vector fields, neutral evolution equations subject to vector measures as impulsive forces, stochastic evolution equations, and optimal control of evolution equations. The optimal control problems considered cover the existence of solutions, necessary conditions of optimality, and more, significantly complementing the existing literature.
This book will be of great interest to researchers in functional analysis, partial differential equations, dynamic systems and their optimal control, and their applications, advancing previous research and providing a foundation for further exploration of the field.

Presents existence of measure-valued solutions for differential equations having no solutions in the usual sense Convers standard and nonstandard optimal control problems Provides nontrivial examples of applications to physical and engineering sciences

Autorentext

N.U. Ahmed is Emeritus Professor at the University of Ottawa. He has made significant contributions to functional analysis applied to systems and optimal control theory. Over his academic career, Dr. Ahmed has published 7 monographs and numerous journal articles in the general areas of systems and control theory, including partial differential equations, stochastic differential equations, abstract differential equations, integral equations and functional analysis. He received the University of Ottawa George Glinski award for excellence in research in 1989. Shian Wang is a senior graduate student at the University of Ottawa. His research interests span the broad area of systems and control theory with extensive applications to intelligent transportation systems.

Klappentext

• 1. Background Materials From Analysis. - 2. Measure Solutions for Deterministic Evolution Equations. - 3. Measure Solutions for Impulsive Systems. - 4. Measure Solutions for Stochastic Systems. - 5. Measure Solutions for Neutral Evolution Equations. - 6. Optimal Control of Evolution Equations. - 7. Examples From Physical Sciences.

  Inhalt

  • 1. Background Materials From Analysis. - 2. Measure Solutions for Deterministic Evolution Equations. - 3. Measure Solutions for Impulsive Systems. - 4. Measure Solutions for Stochastic Systems. - 5. Measure Solutions for Neutral Evolution Equations. - 6. Optimal Control of Evolution Equations. - 7. Examples From Physical Sciences.