Generalized Solution to a Semilinear Hyperbolic System with a Non-Lipshitz Nonlinearity.
Generalized Solutions to Semilinear Hyperbolic Systems.
Genuinely multi-dimensional non-dissipative finite-volume schemes for transport
We develop a new multidimensional finite-volume algorithm for transport equations. This algorithm is both stable and non-dissipative. It is based on a reconstruction of the discrete solution inside each cell at every time step. The proposed reconstruction, which is genuinely multidimensional, allows recovering sharp profiles in both the direction of the transport velocity and the transverse direction. It constitutes an extension of the one-dimensional reconstructions analyzed in (Lagoutière, 2005;...
Global Existence for Quasi-Linear Dissipative Wave Equations with Large Data and Small Parameter.
Global existence for the nonlinear equations of crystal optics
Global smooth solutions of some quasi-linear hyperbolic systems with large data