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Communications in Mathematical Sciences
Volume 18 (2020)
Number 6
Inviscid limit to the shock waves for the fractal Burgers equation
Pages: 1477 – 1491
DOI: https://dx.doi.org/10.4310/CMS.2020.v18.n6.a1
Authors
Abstract
We show the vanishing viscosity limit to entropy shocks for the fractal Burgers equation in one space dimension. More precisely, we quantify the rate of convergence of the inviscid limit in $L^2$ for large initial perturbations around the entropy shock on any bounded time interval. This is the first result on the inviscid limit to entropy shock for the fractal Burgers equation with the quantified convergence, for large initial perturbations.
Keywords
fractal Burgers equation, fractional Laplacian, scalar conservation laws, shock waves, inviscid limit, large perturbation, relative entropy
2010 Mathematics Subject Classification
35L65, 35L67, 35S11, 47G20, 47G30
Received 5 August 2019
Accepted 6 January 2020
Published 4 November 2020