Abstract: We define a class of nonlinear scalar hyperbolic equations on
Riemannian varieties (compact, without boundary). Proofs of existence and
uniqueness are obtained by a combination of dissipative estimates and Young
measures. Suitable entropy conditions are introduced. We show the
convergence of a class of finite-volume schemes and present some numerical
results.
(Joint work with J. Falcovitz and Ph. LeFloch)