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

Ahmed, N. U., Wang, Shian

  • 出版商: Springer
  • 出版日期: 2024-08-13
  • 售價: $4,970
  • 貴賓價: 9.5$4,722
  • 語言: 英文
  • 頁數: 227
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 303137262X
  • ISBN-13: 9783031372629
  • 海外代購書籍(需單獨結帳)

相關主題

商品描述

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.

商品描述(中文翻譯)

本書首次全面介紹了在無限維巴拿赫空間上,非線性確定性和隨機演化方程的測度值解。與傳統解不同,測度值解允許處理更廣泛的抽象演化方程,提供了更廣泛的方法。

本書詳細介紹了對於在通常意義下沒有解的微分方程的測度值解存在性的廣泛結果。內容涵蓋多個主題,包括具有連續/不連續向量場的演化方程、受向量測度作為衝擊力的中性演化方程、隨機演化方程以及演化方程的最佳控制。所考慮的最佳控制問題涵蓋了解的存在性、最優性必要條件等,顯著補充了現有文獻。

本書將對功能分析、偏微分方程、動態系統及其最佳控制及應用領域的研究者產生極大興趣,推進先前的研究並為該領域的進一步探索提供基礎。

作者簡介

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.

作者簡介(中文翻譯)

N. U. Ahmed 是渥太華大學的名譽教授。他在應用於系統和最佳控制理論的函數分析方面做出了重要貢獻。在他的學術生涯中,Ahmed 博士發表了 8 本專著和多篇期刊文章,涵蓋系統與控制理論的一般領域,包括偏微分方程、隨機微分方程、抽象微分方程、積分方程和函數分析。他於 1989 年獲得渥太華大學 George Glinski 研究卓越獎。

Shian Wang 是德克薩斯大學埃爾帕索分校 (UTEP) 的助理教授。Wang 博士在控制系統領域發表了 1 本專著和一系列期刊文章,並應用於智慧交通系統。他於 2023 年獲得德克薩斯大學系統的 Rising STARs 獎。