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The theory of nonlinear hyperbolic equations in several space dimensions has recently obtained remarkable achievements thanks to ideas and techniques related to the structure and fine properties of functions of bounded variation. This volume provides an up-to-date overview of the status and perspectives of two areas of research in PDEs, related to hyperbolic conservation laws. Geometric and measure theoretic tools play a key role to obtain some fundamental advances: the well-posedness theory of linear transport equations with irregular coefficients, and the study of the BV-like structure of bounded entropy solutions to multi-dimensional scalar conservation laws. The volume contains surveys of recent deep results, provides an overview of further developments and related open problems, and will capture the interest of members both of the hyperbolic and the elliptic community willing to explore the intriguing interplays that link their worlds. Readers should have basic knowledge of PDE and measure theory.

Conservation laws (Mathematics) --- Differential equations, Hyperbolic. --- Hyperbolic differential equations --- Differential equations, Partial --- Differential equations, Hyperbolic --- Differential equations, partial. --- Differential Equations. --- Mathematical optimization. --- Mathematics. --- Partial Differential Equations. --- Ordinary Differential Equations. --- Calculus of Variations and Optimal Control; Optimization. --- Measure and Integration. --- Math --- Science --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Maxima and minima --- Operations research --- Simulation methods --- System analysis --- 517.91 Differential equations --- Differential equations --- Partial differential equations --- Partial differential equations. --- Differential equations. --- Calculus of variations. --- Measure theory. --- Lebesgue measure --- Measurable sets --- Measure of a set --- Algebraic topology --- Integrals, Generalized --- Measure algebras --- Rings (Algebra) --- Isoperimetrical problems --- Variations, Calculus of

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The aim of this volume is to provide a synthetic account of past research, to give an up-to-date guide to current intertwined developments of control theory and nonsmooth analysis, and also to point to future research directions.

Control theory --- Nonsmooth optimization --- Systems engineering --- Engineering systems --- System engineering --- Engineering --- Industrial engineering --- System analysis --- Nonsmooth analysis --- Optimization, Nonsmooth --- Mathematical optimization --- Dynamics --- Machine theory --- Research. --- Design and construction

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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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