Global convergence of a sticky particle method for the modified Camassa-Holm equation

Published

Journal Article

© 2017 Society for Industrial and Applied Mathematics. In this paper, we prove convergence of a sticky particle method for the modified Camassa-Holm equation (mCH) with cubic nonlinearity in one dimension. As a byproduct, we prove global existence of weak solutions u with regularity: u and ux are space-time BV functions. The total variation of m(•, t) = u(•, t) - uxx(•, t) is bounded by the total variation of the initial data m0. We also obtain W1,1(ℝ)-stability of weak solutions when solutions are in L∞ (0, ∞; W1,2(ℝ)). (Notice that peakon weak solutions are not in W1,2(ℝ).) Finally, we provide some examples of nonuniqueness of peakon weak solutions to the mCH equation.

Full Text

Duke Authors

Cited Authors

  • Gao, Y; Liu, JG

Published Date

  • January 1, 2017

Published In

Volume / Issue

  • 49 / 2

Start / End Page

  • 1267 - 1294

Electronic International Standard Serial Number (EISSN)

  • 1095-7154

International Standard Serial Number (ISSN)

  • 0036-1410

Digital Object Identifier (DOI)

  • 10.1137/16M1102069

Citation Source

  • Scopus