arXiv Analytics

Sign in

arXiv:1801.01784 [math.AP]AbstractReferencesReviewsResources

Vanishing Viscosity Limits of Scalar Equations with Degenerate Diffusivity

Giuseppe Coclite, Andrea Corli, Lorenzo di Ruvo

Published 2018-01-05Version 1

We consider a scalar, possibly degenerate parabolic equation with a source term, in several space dimensions. For initial data with bounded variation we prove the existence of solutions to the initial-value problem. Then we show that these solutions converge, in the vanishing-viscosity limit, to the Kruzhkov entropy solution of the corresponding hyperbolic equation. The proof exploits the H-measure compactness in several space dimensions.

Comments: 11 pages
Categories: math.AP
Subjects: 35K65, 35L65, 35B25
Related articles: Most relevant | Search more
arXiv:1504.00163 [math.AP] (Published 2015-04-01)
NonLocal Systems of Balance Laws in Several Space Dimensions with Applications to Laser Technolog
arXiv:1303.1699 [math.AP] (Published 2013-03-07, updated 2014-02-05)
Local well-posedness for the nonlinear Dirac equation in two space dimensions
arXiv:math/0703873 [math.AP] (Published 2007-03-29)
A weighted Moser-Trudinger inequality and its relation to the Caffarelli-Kohn-Nirenberg inequalities in two space dimensions

Links

Toolbox