Shock interactions for the Burgers-Hilbert equation

Alberto Bressan, Sondre T. Galtung, Katrin Grunert, Khai T. Nguyen

Research output: Contribution to journalArticlepeer-review

2 Scopus citations

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 (Formula presented.) 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.

Original languageEnglish (US)
Pages (from-to)1795-1844
Number of pages50
JournalCommunications in Partial Differential Equations
Volume47
Issue number9
DOIs
StatePublished - 2022

All Science Journal Classification (ASJC) codes

  • Analysis
  • Applied Mathematics

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