On scalar conservation laws with point source and discontinuous flux function. (English) Zbl 0852.35094

The author considers a scalar conservation law with a nonlinear and discontinuous flux function and an inhomogeneity in form of a delta function like time dependent flux term; the system arises in modelling of continuous sedimentation of solid particles in a liquid. Necessary and also sufficient conditions are given such that the equation has piecewise smooth solutions (constructed by the method of characteristics). A coupling condition on the time axis \(x= 0\) (being a generalization of the classical entropy condition) enforces the solution to be unique.
Reviewer: H.Lange (Köln)


35L65 Hyperbolic conservation laws
35R05 PDEs with low regular coefficients and/or low regular data
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