Brunello Terreni (1953-2000) was a researcher and teacher with vision and dedication. The present volume is dedicated to the memory of Brunello Terreni. His mathematical interests are reflected in 20 expository articles written by distinguished mathematicians. The unifying theme of the articles is "evolution equations and functional analysis", which is presented in various and diverse forms: parabolic equations, semigroups, stochastic evolution, optimal control, existence, uniqueness and regularity of solutions, inverse problems as well as applications. Contributors: P. Acquistapace, V. Barbu, A. Briani, L. Boccardo, P. Colli Franzone, G. Da Prato, D. Donatelli, A. Favini, M. Fuhrmann, M. Grasselli, R. Illner, H. Koch, R. Labbas, H. Lange, I. Lasiecka, A. Lorenzi, A. Lunardi, P. Marcati, R. Nagel, G. Nickel, V. Pata, M. M. Porzio, B. Ruf, G. Savaré, R. Schnaubelt, E. Sinestrari, H. Tanabe, H. Teismann, E. Terraneo, R. Triggiani, A. Yagi

?- Convergence for Infinite Dimensional Optimal Control Problems.- A Degenerate Two-point Problem.- Bounded Solutions for a Class of Quasi-linear Parabolic Problems with a Quadratic Gradient Term.- Degenerate Evolution Systems Modeling the Cardiac Electric Field at Micro- and Macroscopic Level.- Singular Limits for Nonlinear Hyperbolic Systems.- Bounded Perturbations of Ornstein-Uhlenbeck Semigroups.- Degenerate Integrodifferential Equations of Volterra Type in Banach Space.- On a Class of Quasi Linear Equations in Infinite-dimensional Spaces.- Uniform Attractors of Nonautonomous Dynamical Systems with Memory.- On some Mathematical Aspects of the Ring Cavity Problem.- Hadamard Well-posedness of Weak Solutions in Nonlinear Dynamic Elasticity-full von Karman Systems.- Applications des sommes d'opérateurs dans l'étude du comportement singulier des solutions dans les problèmes elliptiques.- Some Identification Problems Related to Thermal Materials with Loss of Memory.- On Generators of Noncommuting Semigroups: Sums, Interpolation, Regularity.- Well-posedness for Nonautonomous Abstract Cauchy Problems.- The Cauchy Problem for a Semilinear Heat Equation with Singular Initial Data.- Well-posedness and Asymptotic Behaviour of Non-autonomous Linear Evolution Equations.- Abstract Hyperbolic Equations in Non-reflexive Spaces.- Min-Max Game Theory and Optimal Control with Indefinite Cost under a Singular Estimate for eAtB in the Absence of Analyticity.- Quasilinear Abstract Parabolic Evolution Equations with Applications.