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Inviscid limit to the shock waves for the fractal Burgers equation. (English) Zbl 1462.35200

Summary: 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.

MSC:

35L67 Shocks and singularities for hyperbolic equations
35L65 Hyperbolic conservation laws
47G20 Integro-differential operators
47G30 Pseudodifferential operators
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