A note on the jump conditions for systems of conservation laws

摘要

In [1], the authors have demonstrated the effect on the Rankine-Hugoniot conditions for a system of conservation laws driven by a singular forcing function and have applied their results to a problem in water waves. We analyze here I similar problem in several space dimensions, in which the singularity in the forcing term involves a simple layer potential supported along the singularity locus. A classical theorem in electrostatics appears as a special case. [References: 6]