Rinaldo M. Colombo

Professor of Mathematical Analysis, University of Brescia^*†‡

INdAM Unit c/o Department of Information Engineering University of Brescia Via Branze 38 25123 Brescia, Italy Phone: [+] 39 030 371 5460 E-mail: Rinaldo.Colombo (at) UniBs.It URL: rinaldo-colombo.unibs.it/ LinkedIn: linkedin.com/in/rinaldo-colombo/

Research

My research focuses on analytical problems arising in hyperbolic conservation laws and motivated by real-world applications. These problems include fundamental questions of well-posedness and stability, as well as optimal control problems and differential games, typically in non-cooperative settings.

I am particularly interested in the formulation and analysis of mathematical models inspired by

• crowd dynamics, such as classroom evacuation and lane formation;
• traffic flow;
• biology, including epidemics (e.g. Covid-19 related research) and vaccination strategies;
• interactions between individuals and populations, including Pied Piper-type models and the control of sheep by dogs, also in settings not involving partial differential equations;
• gas dynamics, including the interaction of a shock wave with a piston;
• mixed hyperbolic-parabolic models for predator-prey interactions and hunting;
• phase transitions and combustion;
• granular matter.

At a purely analytical level, I investigated the well posedness of various problems related to balance laws. In the last years, I got involved in reachability problems and inverse design for conservation laws and Hamilton - Jacobi equations, here and here are sample results.

More recently, I have begun investigating the use of partial differential equations for the encryption and decryption of text messages and images. Results in this direction are published, e.g., here, here and here. Further work is currently in progress.

A complete list of my publications is available. Additional information about my research can be found on MathSciNet, zbMATH Open, ORCID, Scopus and Web of Science.

Editorial Activity

Collaborations (MathSciNet Co-authors)

Meetings & Conferences

Links