In this paper we study the two-dimensional version of the Runge-Kutta Local Projection
Discontinuous Galerkin (RKDG) methods, already defined and analyzed in the one …

The main purpose of this chapter is to give a derivation, which is mathematically precise,
physically natural, and conceptually simple, of the quasilinear system of partial differential …

This is the second edition of a well-received book providing the fundamentals of the theory
hyperbolic conservation laws. Several chapters have been rewritten, new material has been …

During recent years the authors and collaborators have been involved in an activity related
to the construction and analysis of large time step operator splitting algorithms for the …

This set of lecture notes was written for a Nachdiplom-Vorlesungen course given at the
Forschungsinstitut fUr Mathematik (FIM), ETH Zurich, during the Fall Semester 2000. I would …

The use of multiresolution decompositions in the context of finite volume schemes for
conservation laws was first proposed by A. Harten for the purpose of accelerating the …

We study nonlinear degenerate parabolic equations where the flux function f (x, t, u) does
not depend Lipschitz continuously on the spatial location x. By properly adapting the" …

We give a synthetic statement of Kružkov-type estimates for multi-dimensional scalar
conservation laws. We apply it to obtain various estimates for different approximation …

We are concerned with multidimensional stochastic balance laws. We identify a class of
nonlinear balance laws for which uniform spatial BV bound for vanishing viscosity …

An alternative to Glimm's proof of the existence of solutions to systems of hyperbolic
conservation laws is presented. The proof is based on an idea by Dafermos for the single …