TY - JOUR
T1 - Existence and stability for mathematical models of sedimentation-consolidation processes in several space dimensions
AU - Bürger, R.
AU - Liu, C.
AU - Wendland, W. L.
N1 - Funding Information:
We acknowledge support by the Collaborative Research Programme (Sonderforschungs-bereich) 404 “Mehrfeldprobleme in der Kontinuumsmechanik” at the University of Stuttgart. Part of this work was carried out when C. Liu was visiting the Institute of Mathematics A of the University of Stuttgart. C. Liu is further partially supported by NSF Grant DMS-9972040.
PY - 2001/12/15
Y1 - 2001/12/15
N2 - In this paper, we study several spatially multidimensional initial-boundary value problems modelling sedimentation-consolidation processes of a flocculated suspension. This solid-fluid mixture is considered as two superimposed continuous media differing in density and viscosity. The phenomenological foundation and derivation of the mathematical model are based on the previous work by R. Bürger et al. (2000, Z. Angew. Math. Mech. 80, 79-92). We study the full coupling of the conservation of mass equation and the conservation of linear momentum equation. For different types of regularization, we establish energy estimates. The dissipative nature of the whole system assures the existence as well as the stability (long time asymptotics) of a solution of the system (provided that the viscosities of the fluid are large enough). Moreover, the energy estimates might serve as the foundation for the design of numerical algorithms to simulate the system.
AB - In this paper, we study several spatially multidimensional initial-boundary value problems modelling sedimentation-consolidation processes of a flocculated suspension. This solid-fluid mixture is considered as two superimposed continuous media differing in density and viscosity. The phenomenological foundation and derivation of the mathematical model are based on the previous work by R. Bürger et al. (2000, Z. Angew. Math. Mech. 80, 79-92). We study the full coupling of the conservation of mass equation and the conservation of linear momentum equation. For different types of regularization, we establish energy estimates. The dissipative nature of the whole system assures the existence as well as the stability (long time asymptotics) of a solution of the system (provided that the viscosities of the fluid are large enough). Moreover, the energy estimates might serve as the foundation for the design of numerical algorithms to simulate the system.
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U2 - 10.1006/jmaa.2001.7646
DO - 10.1006/jmaa.2001.7646
M3 - Article
AN - SCOPUS:0035894766
SN - 0022-247X
VL - 264
SP - 288
EP - 310
JO - Journal of Mathematical Analysis and Applications
JF - Journal of Mathematical Analysis and Applications
IS - 2
ER -