Shock interactions for the Burgers-Hilbert Equation
Analysis of PDEs
2024-03-06 v1
Abstract
This paper provides an asymptotic description of a solution to the Burgers-Hilbert equation in a neighborhood of a point where two shocks interact. The solution is obtained as the sum of a function with regularity away from the shocks plus a corrector term having an asymptotic behavior like |x|ln|x| close to each shock. A key step in the analysis is the construction of piecewise smooth solutions with a single shock for a general class of initial data.
Cite
@article{arxiv.2204.02421,
title = {Shock interactions for the Burgers-Hilbert Equation},
author = {Alberto Bressan and Sondre T. Galtung and Katrin Grunert and Khai T. Nguyen},
journal= {arXiv preprint arXiv:2204.02421},
year = {2024}
}
Comments
47 pages