Nonlinear Hyperbolic Conservation Laws on Manifolds

Explore nonlinear scalar hyperbolic equations on Riemannian varieties in this 48-minute conference talk delivered by Matania Ben-Artzi at the Erwin Schrödinger International Institute for Mathematics and Physics. Delve into the definition of a class of these equations on compact Riemannian varieties without boundaries. Learn about the proofs of existence and uniqueness obtained through a combination of dissipative estimates and Young measures. Discover the introduction of suitable entropy conditions and their significance. Examine the convergence of a class of finite-volume schemes and observe numerical results presented during the talk. This presentation, part of the Thematic Programme on "The Dynamics of Planetary-scale Fluid Flows," also covers joint work with J. Falcovitz and Ph. LeFloch, providing insights into cutting-edge research in the field of nonlinear hyperbolic conservation laws on manifolds.