On Strongly Degenerate Convection–Diffusion Problems Modeling Sedimentation–Consolidation Processes

By Raimund Bürger, S. Evje, Kenneth Hvistendahl Karlsen. 2000

77 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/31d29e6781f8af4ccffb217eb2f75ee088ceb2fe

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

A note on the uniqueness of entropy solutions of nonlinear degenerate parabolic equations (2002, background): “[2], Karlsen and Risebro [14], Bürger and Karlsen [3], and Mascia et al.”
Nonhomogeneous Dirichlet Problems for Degenerate Parabolic-Hyperbolic Equations (2002, background): “Other results are contained in [3], for the 1-dimensional case again with homogeneous boundary data, and in [4, 5 ] for some applicative models with boundary conditions different with respect to (1.2).”
On some upwind difference schemes for the phenomenological sedimentation-consolidation model (2001, methodology): “It should be pointed out that the new stability and uniqueness proof detailed in [4] is not based on a jump condition, in contrast to the uniqueness proof by Wu and Yin [6].”
On the well-posedness of entropy solutions to conservation laws with a zero-flux boundary condition (2007, unknown): “Existence of entropy solutions To show the existence of an entropy solution (in the sense of the previous section), we consider as in [2] the following regularized parabolic problem for each ε > 0: ∂tu ε + ∇x · f ( u ) = ε u, (x, t) ∈ QT , (4.”
QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC EQUATIONS WITH TIME-SPACE DEPENDENT DIFFUSION COEFFICIENTS (2005, background): “To mention just a few examples, other extensions can be found in [8, 23, 29, 30, 31, 35].”
On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients (2003, background): “In [ 7 ] (see also [29]), the uniqueness proof of Carrillo was adopted to several initial-boundary value problems arising the theory of sedimentation-consolidation processes [9], which in some cases call for the notion of an entropy boundary condition (see also [8] for the BV approach).”
Renormalized entropy solutions of homogeneous Dirichlet problems for quasilinear anisotropic degenerate parabolic-hyperbolic equations (2012, background): “Various extensions of his important result can be found in [11,23,24].”