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arXiv · 2204.02421

Shock interactions for the Burgers-Hilbert Equation

Alberto Bressan·Sondre T. Galtung·Katrin Grunert·Khai T. Nguyen
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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 $H^2$ 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.

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Alberto Bressan, Sondre T. Galtung, Katrin Grunert, Khai T. Nguyen. 2022-04-05. Shock interactions for the Burgers-Hilbert Equation. https://doi.org/10.1080/03605302.2022.2084628

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