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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.
List of contents
- 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.
About the author
N. U. Ahmed is an 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 8 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 an Assistant Professor at The University of Texas at El Paso (UTEP). Dr. Wang has published 1 monograph and a series of journal articles in the area of control systems with application to intelligent transportation systems. He received a Rising STARs Award from The University of Texas System in 2023.
Report
The monograph and the topics covered here are very useful for specialists in differential equations and systems theory in general. This can be classified as a call for mathematicians, especially recent graduates, to get involved in measure solution research. ... I congratulate the authors who point out a new perspective in systems theory. (Agamirza E. Bashirov, Mathematical Reviews, May, 2025)
