Publications [#329525] of Jian-Guo Liu

Papers Published

1. Gao, Y; Liu, JG, Global convergence of a sticky particle method for the modified Camassa-Holm equation, SIAM Journal on Mathematical Analysis, vol. 49 no. 2 (January, 2017), pp. 1267-1294, Society for Industrial & Applied Mathematics (SIAM) [doi]
   (last updated on 2025/05/01)

   Abstract:
   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.