This book, based on a selection of talks given at a dedicated meeting in Cortona, Italy, in June 2013, shows the high degree of interaction between a number of fields related to applied sciences. Applied sciences consider situations in which the evolution of a given system over time is observed, and the related models can be formulated in terms of evolution equations (EEs). These equations have been studied intensively in theoretical research and are the source of an enormous number of applications. In this volume, particular attention is given to direct, inverse and control problems for EEs. The book provides an updated overview of the field, revealing its richness and vitality.
1 F. Alabau-Boussouira, S. Nicaise and C. Pignotti: Exponential stability of the wave equation with memory and time delay.- 2 Fabio Ancona and Giuseppe Maria Coclite: Existence of global weak solutions to a generalized hyperelastic-rod wave equation with source.- 3 George Avalos and Francesca Bucci: Exponential decay properties of a mathematical model for a certain fluid-structure interaction.- 4 Karine Beauchard and Piermarco Cannarsa: Inverse coefficient problem for Grushin-type parabolic operators.- 5 Mourad Choulli, Kian Yavar and Eric Soccorsi: Determining the scalar potential in a periodic quantum waveguide from the DN map.- 6 Angelo Favini, Alfredo Lorenzi and Hiroki Tanabe: A general approach to identification problems.- 7 Genni Fragnelli, Gabriela Marinoschi, Rosa Maria Mininni and Silvia Romanelli: A control approach for an identification problem associated to a strongly degenerate parabolic system with interior degeneracy.- 8 Jerome A. Goldstein and Junqiang Han: On the Nature of the Instability of Radial Power Equilibria of a Semilinear Parabolic Equation.- 9 Davide Guidetti: Abstract elliptic problems depending on a parameter and parabolic problems with dynamic boundary conditions.- 10 Victor Isakov: Increasing stability of the continuation for general elliptic equations of second order.- 11 Vilmos Komornik and Paola Loreti: Simultaneous observability of plates.- 12 Markus Kunze, Luca Lorenzi and Abdelaziz Rhandi: Kernel estimates for nonautonomous Kolmogorov equations with potential term.- 13 Galina Kurina: On Some Inverse Problems of the Calculus of Variations for Second Order Differential Equations with Deviating Arguments and Partial Derivatives.- 14 Irena Lasiecka and XiaojunWang: Intrinsic Decay Rate Estimates for Semilinear Abstract Second Order Equations with Memory.- 15 Shitao Liu and Roberto Triggiani: Inverse problem for a linearized JordanMooreGibsonThompson equation.- 16 Irina V. Melnikova, Uliana A. Alekseeva and Vadim A. Bovkun: Solutions of Stochastic Systems generalized over temporal and spatial variables.- 17 Gianluca Mola: Recovering the reaction coefficient in a linear parabolic equation.- 18 Noboru Okazawa and Motohiro Sobajima: LP-theory for Schrodinger operators perturbed by singular drift terms.- 19 Ioan I. Vrabie: Semilinear delay evolution equations with nonlocal initial conditions.- 20 Yakov Yakubov: Elliptic differential-operator problems with the spectral parameter in both the equation and boundary conditions and the corresponding abstract parabolic initial boundary value problems.