On the Convergence of Quasilinear Viscous Approximations with Degenerate Viscosity

2023/01/17 by Mondal, Ramesh
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2301.07011

Abstract

We use Velocity Averaging lemma to show that the almost everywhere limit of quasilinear viscous approximations is the unique entropy solution (in the sense of \it F. Otto) of the corresponding scalar conservation laws on a bounded domain in ℝ^d, where the viscous term is of the form ε div(B(u^ε)∇ u^ε) and B≥ 0.

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