Provides a collection of contributions honouring Professor Gianni Gilardi

Discusses well-posedness and optimal control problems with reference to applied sciences

Offers a survey of the most recent results in the field

Autorentext

Prof. Pierluigi Colli graduated in Mathematics at the University of Pavia in 1981, before becoming a researcher and associate professor at the same university. He evolved into professor of mathematical analysis at the University of Torino in 1994, and then he moved back to Pavia in 1998. He is author or coauthor of more than 150 papers, and co-editor of six special volumes. His main research area is the mathematical analysis of nonlinear evolution problems, in particular parabolic systems of partial differential equations arising from differential models in physics, thermodynamics, mechanics and physiology. Prof. Angelo Favini was an assistant professor from 1971 to 1976, and has been a professor at the University of Bologna since then. He is the author of 230 publications in international journals, mainly devoted to interpolation, differential equations in Banach spaces, partial differential equations, control theory and ill-posed problems. His main research focus ison degenerate equations, and he has written a monograph on this subject with A. Yagi (Osaka). He is also the author of a monograph on nonlinear diffusion equations with G. Marinoschi (Bucarest), Springer Verlag 2012.

Prof. Elisabetta Rocca graduated in Mathematics in 1999 at the University of Pavia, where she also obtained her PhD in 2004. She was a researcher at the University of Milan till 2011 when she became associate professor. She moved to the WIAS in Berlin in 2013 where she spent 2 years coordinating a research group with the ERC Starting Grant she received as PI in 2011. She moved to the University of Pavia in 2016 where she is associate professor. She is author of more than 80 papers in mathematical analysis and applications.

Prof. Giulio Schimperna obtained his PhD in Mathematics at Milan University in 2000. Since 2006 he has been a professor of mathematical analysis in Pavia. He has authored more than 70 papers publishedin international scientific journals. His scientific interests mainly focus on the analysis of nonlinear evolutionary partial differential equations, and, in particular, mathematical models for phase transitions, damaging, thermomechanics and complex fluids.

Prof. Jürgen Sprekels graduated in 1972 in Mathematics at the University of Hamburg (Germany), where he also received his Ph.D. in 1975. He was a professor at the universities of Augsburg and Essen, before moving to a full professorship at the Humboldt University "at zu Berlin" in 1994. From 1994 to 2015, he was also the director of the Weierstrass Institute (WIAS) in Berlin. He is the coauthor of two monographs, co-editor of several conference proceedings, and coauthor of nearly 200 research papers in various fields of applied mathematics.

Klappentext
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.

Inhalt

1 Rate of convergence for eigenfunctions of Aharonov-Bohm operators with a moving pole.- 2 Nondecreasing solutions to doubly nonlinear equations.- 3 Identification problems for degenerate integro-differential equations.- 4 A phase transition model describing auxetic materials.- 5 Global well-posedness for a phase transition model with irreversible evolution and acceleration forces.- 6 Perimeter symmetrization of some dynamic and stationary equations involving the Monge-Ampere operator.- 7 Optimal boundary control of a nonstandard Cahn-Hilliard system with dynamic boundary condition and double obstacle inclusions.- 8 Nontrivial solutions of quasilinear elliptic equatons with natural growth term .- 9 On a diffuse interface model for tumour growth with non-local interactions and degenerate mobilities.- 10 A boundary control problem for the equation and dynamic boundary condition of Cahn-Hilliard type.- 11 New class of doubly nonlinear evolution equations governed by time-dependent subdifferentials.- 12 Boundedness of solutions to a degenerate diffusion equation.- 13 Optimal a priori error estimates of parabolic optimal control problems with a moving point control.- 14 A note on the feedback stabilization of a Cahn-Hilliard type system with a singular logarithmic potential.- 15 Mathematical analysis of a parabolic-elliptic model for brain lactate kinetics.- 16 Weak formulation for singular diffusion equation with dynamic boundary condition.- 17 Smooth and broken minimizers of some free discontinuity problems.- 18 Stability results for abstract evolution equations with intermittent time-delay feedback.- 19 From visco-energetic to energetic and balanced viscosity solutions of rate-independent systems.- 20 A duality approach in some boundary value problems.- 21 On the structural properties of nonlinear flows.