Details

Autor(en) / Beteiligte

• Diehl, Stefan

Titel

A Conservation Law with Point Source and Discontinuous Flux Function Modelling Continuous Sedimentation

Ist Teil von

• SIAM journal on applied mathematics, 1996-04, Vol.56 (2), p.388-419

Ort / Verlag

Philadelphia: Society for Industrial and Applied Mathematics

Erscheinungsjahr

1996

Link zum Volltext

Quelle

Alma/SFX Local Collection

Beschreibungen/Notizen

• Continuous sedimentation of solid particles in a liquid takes place in a clarifier-thickener unit, which has one feed inlet and two outlets. The aim of the paper is to formulate and analyse a dynamic model for this process under idealized physical conditions. The conservation of mass yields the scalar conservation law ∂ u(x, t)/∂ t + ∂/∂ x (F(u(x, t), x)) = s(t)δ (x), where δ is the Dirac measure, s is a source, and F is a flux function, which is discontinuous at three points in the one-dimensional space coordinate x. Under certain regularity assumptions a procedure for constructing a solution, locally in time, is presented. The nonlinear phenomena are complicated, and so is the general construction of a solution. The problem of nonuniqueness due to the discontinuities of$F(u, \centerdot)$is handled by a generalized entropy condition. An advantage of this approach is that the a priori boundary conditions (at the discontinuities of F(u, ·)) that have been used earlier can be omitted. The steady-state solutions are also presented.