GLOBAL CONVERGENCE OF A STICKY PARTICLE METHOD FOR THE MODIFIED CAMASSA–HOLM EQUATION.
In: SIAM Journal on Mathematical Analysis, Jg. 49 (2017-04-01), Heft 2, S. 1267-1294
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Zugriff:
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,∞;W2,1(ℝ)). (Notice that peakon weak solutions are not in W2,1(ℝ).) Finally, we provide some examples of nonuniqueness of peakon weak solutions to the mCH equation. [ABSTRACT FROM AUTHOR]
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GLOBAL CONVERGENCE OF A STICKY PARTICLE METHOD FOR THE MODIFIED CAMASSA–HOLM EQUATION.
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Autor/in / Beteiligte Person: | YU, GAO ; JIAN-GUO, LIU |
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Zeitschrift: | SIAM Journal on Mathematical Analysis, Jg. 49 (2017-04-01), Heft 2, S. 1267-1294 |
Veröffentlichung: | 2017 |
Medientyp: | academicJournal |
ISSN: | 0036-1410 (print) |
DOI: | 10.1137/16M1102069 |
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