Vanishing Viscosity Limits of Scalar Equations with Degenerate Diffusivity
Analysis of PDEs
2018-01-08 v1
Abstract
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.
Keywords
Cite
@article{arxiv.1801.01784,
title = {Vanishing Viscosity Limits of Scalar Equations with Degenerate Diffusivity},
author = {Giuseppe Coclite and Andrea Corli and Lorenzo di Ruvo},
journal= {arXiv preprint arXiv:1801.01784},
year = {2018}
}
Comments
11 pages