论文标题
汉堡 - 希尔伯特方程的冲击互动
Shock interactions for the Burgers-Hilbert Equation
论文作者
论文摘要
本文在两个冲击相互作用的地方的汉堡 - 希尔伯特方程的解决方案提供了渐近描述。该解决方案作为$ h^2 $规律性的函数总和，远离冲击，以及具有渐近行为的校正术语，例如| x | ln | x |接近每个冲击。分析的关键步骤是对一般初始数据的单一冲击构建分段平滑解决方案。
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.
