English

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}
}

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11 pages