Solvability, Regularity, and Optimal Control of Boundary Value Problems for PDEs: In Honour of Prof. Gianni Gilardi

Description

This volume gathers contributions in the field of partial differential equations, with a focus on mathematical models in phase transitions, complex fluids and thermomechanics. These contributions are dedicated to Professor Gianni Gilardi on the occasion of his 70th birthday. It particularly develops the following thematic areas: nonlinear dynamic and stationary equations; well-posedness of initial and boundary value problems for systems of PDEs; regularity properties for the solutions; optimal control problems and optimality conditions; feedback stabilization and stability results. Most of the articles are presented in a self-contained manner, and describe new achievements and/or the state of the art in their line of research, providing interested readers with an overview of recent advances and future research directions in PDEs. Front Matter ....Pages i-xii Rate of Convergence for Eigenfunctions of Aharonov-Bohm Operators with a Moving Pole (Laura Abatangelo, Veronica Felli)....Pages 1-30 Nondecreasing Solutions to Doubly Nonlinear Equations (Goro Akagi, Ulisse Stefanelli)....Pages 31-53 Identification Problems for Degenerate Integro-Differential Equations (Mohammed Al Horani, Mauro Fabrizio, Angelo Favini, Hiroki Tanabe)....Pages 55-75 A Phase Transition Model Describing Auxetic Materials (Elena Bonetti, Mauro Fabrizio, Michel Frémond)....Pages 77-95 Global Well-Posedness for a Phase Transition Model with Irreversible Evolution and Acceleration Forces (Giovanna Bonfanti, Fabio Luterotti)....Pages 97-117 Perimeter Symmetrization of Some Dynamic and Stationary Equations Involving the Monge-Ampère Operator (Barbara Brandolini, Jesús Ildefonso Díaz)....Pages 119-149 Optimal Boundary Control of a Nonstandard Cahn–Hilliard System with Dynamic Boundary Condition and Double Obstacle Inclusions (Pierluigi Colli, Jürgen Sprekels)....Pages 151-182 Nontrivial Solutions of Quasilinear Elliptic Equations with Natural Growth Term (Marco Degiovanni, Alessandra Pluda)....Pages 183-215 On a Diffuse Interface Model for Tumour Growth with Non-local Interactions and Degenerate Mobilities (Sergio Frigeri, Kei Fong Lam, Elisabetta Rocca)....Pages 217-254 A Boundary Control Problem for the Equation and Dynamic Boundary Condition of Cahn–Hilliard Type (Takeshi Fukao, Noriaki Yamazaki)....Pages 255-280 New Class of Doubly Nonlinear Evolution Equations Governed by Time-Dependent Subdifferentials (Nobuyuki Kenmochi, Ken Shirakawa, Noriaki Yamazaki)....Pages 281-304 Boundedness of Solutions to a Degenerate Diffusion Equation (Pavel Krejčí)....Pages 305-326 Optimal A Priori Error Estimates of Parabolic Optimal Control Problems with a Moving Point Control (Dmitriy Leykekhman, Boris Vexler)....Pages 327-356 A Note on the Feedback Stabilization of a Cahn–Hilliard Type System with a Singular Logarithmic Potential (Gabriela Marinoschi)....Pages 357-377 Mathematical Analysis of a Parabolic-Elliptic Model for Brain Lactate Kinetics (Alain Miranville)....Pages 379-403 Weak Formulation for Singular Diffusion Equation with Dynamic Boundary Condition (Ryota Nakayashiki, Ken Shirakawa)....Pages 405-429 Smooth and Broken Minimizers of Some Free Discontinuity Problems (Danilo Percivale, Franco Tomarelli)....Pages 431-468 Stability Results for Abstract Evolution Equations with Intermittent Time-Delay Feedback (Cristina Pignotti)....Pages 469-487 From Visco-Energetic to Energetic and Balanced Viscosity Solutions of Rate-Independent Systems (Riccarda Rossi, Giuseppe Savaré)....Pages 489-531 A Duality Approach in Some Boundary Value Problems (Dan Tiba)....Pages 533-542 On the Structural Properties of Nonlinear Flows (Augusto Visintin)....Pages 543-571