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 language | English (US) |
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Pages (from-to) | 1795-1844 |
Number of pages | 50 |
Journal | Communications in Partial Differential Equations |
Volume | 47 |
Issue number | 9 |
DOIs | |
State | Published - 2022 |
All Science Journal Classification (ASJC) codes
- Analysis
- Applied Mathematics