Problémes de riemann singuliers

Abstract

One construct simple hyperbolic systems of conservation laws for which some Riemann problem does not have any solution in the distributionnal sense. However those systems are endowed with the best algebraic properties of the theory : they may be strictly hyperbolic with either genuinely nonlinear or linearly degenerate characteristic fields. The study of a viscous profile suggests that a solution would belong on a set of generalized functions. Lastly, one gives a related example in which a solution exists but is unbounded for any positive time

Keywords:

• Hyperbolic systems
• Riemann problems

AMS(MOS):

• 35D05
• 35L60
• 35L65