Vanishing non-local regularization of a scalar conservation law.
Variational particle schemes for the porous medium equation and for the system of isentropic Euler equations
Both the porous medium equation and the system of isentropic Euler equations can be considered as steepest descents on suitable manifolds of probability measures in the framework of optimal transport theory. By discretizing these variational characterizations instead of the partial differential equations themselves, we obtain new schemes with remarkable stability properties. We show that they capture successfully the nonlinear features of the flows, such as shocks and rarefaction waves for...
Viscosity solutions and standard Riemann semigroup for conservation laws with boundary
Viscous profiles for traveling waves of scalar balance laws: The uniformly hyperbolic case.