Math @ Duke

Publications [#329525] of JianGuo Liu
Papers Published
 Gao, Y; Liu, JG, Global convergence of a sticky particle method for the modified CamassaHolm equation,
Siam Journal on Mathematical Analysis, vol. 49 no. 2
(January, 2017),
pp. 12671294, Society for Industrial & Applied Mathematics (SIAM) [doi]
(last updated on 2019/06/24)
Abstract: © 2017 Society for Industrial and Applied Mathematics. In this paper, we prove convergence of a sticky particle method for the modified CamassaHolm 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 spacetime 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.


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