Special Session 24
Conservation Laws for Fluid and Transport Models: Analysis and Numerics
Organizers: Fabio Ancona (University of Padua, Italy), Eduardo Abreu (State University of Campinas, Brazil), Maria Teresa Chiri (Queen’s University, Canada)
MSC codes: 35L65; 35Lxx; 35A35; 35Q89; 65M08; 76-XX: 49N45
Description:
The scope of this Special Session is to bring together researchers working on first-order hyperbolic partial differential equations, including systems of conservation laws, balance laws, non-local models, and control problems, from both theoretical and applied perspectives. The session aims to foster interaction between different mathematical communities and to promote interdisciplinary research bridging modeling, analysis, and numerical computation. The focus is on recent developments in the mathematical and numerical study of conservation laws, with particular attention to applications in fluid dynamics, shallow water models, traffic flow, and related continuum descriptions. Contributions addressing analytical properties, asymptotic regimes, and computational methods are equally welcome. The session will cover, among others, the following topics:
- hyperbolic systems of conservation and balance laws;
- relaxation methods and asymptotic limits;
- fluid dynamics and shallow water equations;
- non-local models in traffic flow and fluid mechanics;
- qualitative and quantitative analysis of solutions;
- numerical analysis and computational methods for hyperbolic PDEs;
- applications involving real-world phenomena.
Conservation laws exhibit complex solution behavior, including wave interactions and shock formation, and play a central role in the modeling of many physical systems. Their intrinsically multidisciplinary nature makes the field particularly suitable for fostering collaborations and for the training of young researchers. This Special Session aims to provide a forum for the exchange of ideas between Italian and Brazilian researchers working on hyperbolic equations and their applications.
