Raimund Bürger

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Abstract. We consider scalar conservation laws with the spatially varying flux H(x)f(u)+(1−H(x))g(u), where H(x) is the Heaviside function and f and g are smooth nonlinear functions. Adimurthi, Mishra, and Veerappa Gowda [J. Hyperbolic Differ. Equ. 2:783–837, 2005] pointed out that such a conservation law admits many L contraction semigroups, one for each(More)
The extension of Kynch’s kinematic theory of sedimentation of monodisperse suspensions to polydisperse mixtures leads to a nonlinear system of conservation laws for the volume fractions of each species. In this paper, we show that a second order central (Riemann solver free) scheme for the solution of systems of conservation laws can be employed as an(More)
We show how existing models for the sedimentation of monodisperse flocculated suspensions and of polydisperse suspensions of rigid spheres differing in size can be combined to yield a new theory of the sedimentation processes of polydisperse suspensions forming compressible sediments (“sedimentation with compression” or “sedimentation-consolidation(More)
The chief purpose of this paper is to formulate and partly analyze a new mathematical model for continuous sedimentation-consolidation processes of flocculated suspensions in clarifierthickener units. This model appears in two variants for cylindrical and variable cross-sectional area units, respectively (Models 1 and 2). In both cases, the governing(More)
The classical Lighthill-Whitham-Richards (LWR) kinematic traffic model is extended to a unidirectional road on which the maximum density a(x) represents road inhomogeneities, such as variable numbers of lanes, and is allowed to vary discontinuously. The car density φ = φ(x, t) is then determined by the following initial value problem for a scalar(More)
We present an initial—boundary value problem of a quasilinear degenerate parabolic equation for the settling and consolidation of a flocculated suspension. The corresponding definition of generalized solutions is formulated. It is based on an entropy integral inequality in the sense of Kruz\ kov. From this definition, jump and entropy conditions that have(More)
We present fully adaptive multiresolution methods for a class of spatially twodimensional reaction-diffusion systems which describe excitable media and often give rise to the formation of spiral waves. A novel model ingredient is a strongly degenerate diffusion term that controls the degree of spatial coherence and serves as a mechanism for obtaining(More)