Trends in Control Theory and Partial Differential Equations

✍ Scribed by Fatiha Alabau-Boussouira, Fabio Ancona, Alessio Porretta, Carlo Sinestrari

• Publisher: Springer International Publishing
• Year: 2019
• Tongue: English
• Leaves: 285
• Series: Springer INdAM Series 32
• Edition: 1st ed.
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Front Matter ....Pages i-xii
Some Remarks on the Dirichlet Problem for the Degenerate Eikonal Equation (Paolo Albano)....Pages 1-16
Lipschitz Continuity of the Value Function for the Infinite Horizon Optimal Control Problem Under State Constraints (Vincenzo Basco, Hélène Frankowska)....Pages 17-38
Herglotz’ Generalized Variational Principle and Contact Type Hamilton-Jacobi Equations (Piermarco Cannarsa, Wei Cheng, Kaizhi Wang, Jun Yan)....Pages 39-67
Observability Inequalities for Transport Equations through Carleman Estimates (Piermarco Cannarsa, Giuseppe Floridia, Masahiro Yamamoto)....Pages 69-87
On the Weak Maximum Principle for Degenerate Elliptic Operators (Italo Capuzzo Dolcetta)....Pages 89-104
On the Convergence of Open Loop Nash Equilibria in Mean Field Games with a Local Coupling (Pierre Cardaliaguet)....Pages 105-122
Remarks on the Control of Family of b–Equations (Enrique Fernández-Cara, Diego A. Souza)....Pages 123-138
1-d Wave Equations Coupled via Viscoelastic Springs and Masses: Boundary Controllability of a Quasilinear and Exponential Stabilizability of a Linear Model (Günter Leugering, Tatsien Li, Yue Wang)....Pages 139-156
A Semilinear Integro-Differential Equation: Global Existence and Hidden Regularity (Paola Loreti, Daniela Sforza)....Pages 157-180
Lyapunov’s Theorem via Baire Category (Marco Mazzola, Khai T. Nguyen)....Pages 181-194
Controllability Under Positivity Constraints of Multi-d Wave Equations (Dario Pighin, Enrique Zuazua)....Pages 195-232
Asymptotic Analysis of a Cucker–Smale System with Leadership and Distributed Delay (Cristina Pignotti, Irene Reche Vallejo)....Pages 233-253
Global Non-negative Approximate Controllability of Parabolic Equations with Singular Potentials (Judith Vancostenoble)....Pages 255-276

✦ Subjects

Mathematics; Partial Differential Equations; Calculus of Variations and Optimal Control; Optimization; Game Theory, Economics, Social and Behav. Sciences