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

Beschreibung

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.
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

Autor*in

N. U. Ahmed

Themen in »Measure-Valued Solutions for Nonlinear Evolution Equations on Banach Spaces and Their Optimal Control«

Abstract Differential Equation Evolution Equation Stochastic Differential Equation on Hilbert Spaces Stochastics Differential Equation Stochastic Navier-Stokes Equation Schrodinger Equation Reaction Diffusion Equation Optimal Control of Nonstandard Problems

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“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)

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