GA1/4nter Lumer was an outstanding mathematician whose work has great influence on the research community in mathematical analysis and evolution equations. He was at the origin of the breath-taking development the theory of semigroups saw after the pioneering book of Hille and Phillips of 1957. This volume contains invited contributions presenting the state of the art of these topics and reflecting the broad interests of GA1/4nter Lumer.

By introducing a new stabilization methodology, this book characterizes the stability of a certain class of systems. The stability (exponential, polynomial, or weaker) for the closed loop problem is reduced to an observability estimate for the corresponding uncontrolled system combined with a boundedness property of the transfer function of the associated open loop system. A similar strategy is applied to systems where a delay term is added. The book concludes with many concrete examples. This book is addressed to graduate students in mathematics or engineering and also to researchers with an interest in stabilization and control systems governed by partial differential equations.

Based on lectures presented at the international conference on Partial Differential Equations (PDEs) on Multistructures, held recently in Lu miny, France. Contains the latest advances in the field, compiling up- to-the-minute research on the analyses and applications of multistruct uresyincluding current treatments of classical theories, specific char acterizations and modelings of multistructures, and timely discussions on uses in physics, electronics, and biology. Highlights nonlinear an d numerical analysis, finite element methods, variational calculus, in tegral equations, and dynamical systems.