Trends in Control Theory and Partial Differential Equations

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.

1 P. Albano, Some remarks on the Dirichlet problem for the degenerate eikonal equation.- 2 V. Basco and H. Frankowska, Lipschitz continuity of the value function for the infinite horizon optimal control problem under state constraints.- 3 P. Cannarsa et al., Herglotz generalized variational principle and contact type Hamilton-Jacobi equations.- 4 P. Cannarsa et al., Observability inequalities for transport equations through Carleman estimates.- 5 I. Capuzzo Dolcetta, On the weak maximum principle for degenerate elliptic operators.- 6 P. Cardaliaguet, On the convergence of open loop Nash equilibria in mean field games with a local coupling.- 7 E. Fernández-Cara and D. A. Souza, Remarks on the control of a family of b-equations.- 8 G. Leugering et al., 1-d wave equations coupled via viscoelastic springs and masses: boundary controllability of a quasilinear and exponential stabilizability of a linear model.- 9 P. Loreti and D. Sforza, A semilinear integro-differential equation: global existence and hidden regularity.- 10 M. Mazzola and K. T. Nguyen, Lyapunovs theorem via Baire category.- 11 D. Pighin and E. Zuazua, Controllability under positivity constraints of multi-d wave equations.- 12 C. Pignotti and I. Reche Vallejo, Asymptotic analysis of a Cucker-Smale system with leadership and distributed delay.- 13 J. Vancostenoble, Global non-negative approximate controllability of parabolic equations with singular potentials.