On the uniqueness and stability of entropy solutions of nonlinear degenerate parabolic equations with rough coefficients

By Kenneth Hvistendahl Karlsen, Nils Henrik Risebro. 2003

177 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/7123040f151cc26dac1afe3446f33ba926da19ef

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In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

On some upwind difference schemes for the phenomenological sedimentation-consolidation model (2001, background): “Following [23], we say that u is an entropy solution of (30) if”
A note on the uniqueness of entropy solutions of nonlinear degenerate parabolic equations (2002, methodology): “This part of the proof follows [ 14 ] closely.”
Finite Volume Methods: Foundation and Analysis (2004, methodology): “In the context of convection dominated or degenerate parabolic equations, Kruzkov techniques have been used by Carrillo (1999) and Karlsen and Risebro (2000) in proving the Encyclopedia of Computational Mechanics.”
Stability and Total Variation Estimates on General Scalar Balance Laws (2008, unknown): “An flow dependent also on x was considered in [4, 9], though in the special case f(x, u) = l(x) g(u), but with a source term containing a possibly degenerate parabolic operator.”
ON A NONLINEAR DEGENERATE PARABOLIC TRANSPORT-DIFFUSION EQUATION WITH A DISCONTINUOUS COEFFICIENT (2002, background): “, [12] it follows that ‖uε(·, t)‖L1(R) ≤ ‖uε(·, 0)‖L1(R) , for all t ∈ (0, T ).”
Asymptotic analysis of an advection-dominated chemotaxis model in multiple spatial dimensions (2008, unknown): “Then, it follows from [18], Theorem 1.”
QUASILINEAR ANISOTROPIC DEGENERATE PARABOLIC EQUATIONS WITH TIME-SPACE DEPENDENT DIFFUSION COEFFICIENTS (2005, methodology): “These terms can be included into the analysis by copying the arguments from [26] (we leave the details to the reader).”
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].”
On Nonlinear Stochastic Balance Laws (2011, methodology): “Relevant continuous dependence results for deterministic conservation laws have been obtained in [17, 2], and in [4] for strongly degenerate parabolic equations; see also [3, 11].”
Upwind difference approximations for degenerate parabolic convection–diffusion equations with a discontinuous coefficient (2002, background): “Existence, uniqueness and stability results for entropy solutions of strongly degenerate parabolic equations with smooth coefficients can be found in [2, 6, 9, 28, 50, 48, 47].”