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This book presents cutting-edge contributions in the areas of control theory and partial differential equations. Over the decades, control theory has had deep and fruitful interactions with the theory of partial differential equations (PDEs). Well-known examples are the study of the generalized solutions of Hamilton-Jacobi-Bellman equations arising in deterministic and stochastic optimal control and the development of modern analytical tools to study the controllability of infinite dimensional systems governed by PDEs. In the present volume, leading experts provide an up-to-date overview of the connections between these two vast fields of mathematics. Topics addressed include regularity of the value function associated to finite dimensional control systems, controllability and observability for PDEs, and asymptotic analysis of multiagent systems. The book will be of interest for both researchers and graduate students working in these areas.

Differential equations, Partial. --- Control theory. --- Differential equations, partial. --- Mathematical optimization. --- Mathematics. --- Partial Differential Equations. --- Calculus of Variations and Optimal Control; Optimization. --- Game Theory, Economics, Social and Behav. Sciences. --- Math --- Science --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- Partial differential equations --- Partial differential equations. --- Calculus of variations. --- Game theory. --- Games, Theory of --- Theory of games --- Mathematical models --- Mathematics --- Isoperimetrical problems --- Variations, Calculus of

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The term control theory  refers to the body of results - theoretical, numerical and algorithmic - which have been developed to influence the evolution of the state of a given system in order to meet a prescribed performance criterion. Systems of interest to control theory may be of very different natures. This monograph is concerned with models that can be described by partial differential equations of evolution. It contains five major contributions and is connected to the CIME Course on Control of Partial Differential Equations that took place in Cetraro (CS, Italy), July 19 - 23, 2010.  Specifically, it covers the stabilization of evolution equations, control of the Liouville equation, control in fluid mechanics, control and numerics for the wave equation, and Carleman estimates for elliptic and parabolic equations with application to control. We are confident this work will provide an authoritative reference work for all scientists who are interested in this field, representing at the same time a friendly introduction to, and an updated account of, some of the most active trends in current research.

Partial differential equations --- Numerical analysis --- Fluid mechanics --- Engineering sciences. Technology --- vloeistofstroming --- differentiaalvergelijkingen --- aerodynamica --- systeemtheorie --- systeembeheer --- numerieke analyse

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Partial differential equations --- Numerical analysis --- Fluid mechanics --- Engineering sciences. Technology --- vloeistofstroming --- differentiaalvergelijkingen --- aerodynamica --- systeemtheorie --- systeembeheer --- numerieke analyse