Measure-Valued Solutions for Nonlinear Evolution Equations on Banach Spaces and Their Optimal Control 1st edition N.u. Ahmed by N.u. Ahmed, Shian Wang 9783031372599, 9783031372605, 303137259X, 3031372603 instant download after payment.

Mathematics Subject Classification: 35A01 Existence problems for PDEs: global existence, local existence, non-existence • 35A02 Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness • 35B44 Blow-up in context of PDEs • 35K57 Reaction-diffusion equations • 35Q30 Navier-Stokes equations • 37N35 Dynamical systems in control • 46G10 Vector-valued measures and integration • 46E27 Spaces of measures • 49J20 Existence theories for optimal control problems involving partial differential equations …

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.