https://www.uevora.pt/pessoas?id=5348
Title: Nonlinear hyperbolic systems of conservation laws: direct and regularized approximation methods
Abstract: This two-week research project focuses on the mathematical analysis of nonlinear hyperbolic systems of conservation laws, which arise in various fields such as fluid dynamics, traffic flow, and gas dynamics. Participants will study the existence, uniqueness, and behavior of weak solutions, including the formation of shocks and discontinuities. The project will explore both direct methods (e.g., Riemann solvers) and regularized approaches (e.g., vanishing viscosity) for approximating solutions. Through theoretical study, and eventually hands-on computational experiments, the group will compare the accuracy, stability, and efficiency of these methods, gaining insight into their applicability across different problem settings.
Prerequisites:
· Basic knowledge of ordinary and partial differential equations (especially in hyperbolic equations will be appreciated),
· Good mathematical analysis knowledge (e.g., implicit function theorem, and divergence theorem),
· Some familiarity with conservation laws with conservation laws will be appreciated,
· Some exposure to regularization techniques.
Group members
Akshay KUMAR
Rani SULVIANURI
Khankham VONGSAVANG
Bounmy KHAMINSOU