On  the blow-up of solutions to the periodic modified integrable Camassa--Holm equation

Min  Zhu; Shuanghu  Zhang

doi:10.3934/dcds.2016.36.2347

Article Contents

2016, Volume 36, Issue 4: 2347-2364. Doi: 10.3934/dcds.2016.36.2347

This issue Previous Article Entire solutions with merging fronts to a bistable periodic lattice dynamical system Next Article Erratum and addendum to: The general recombination equation in continuous time and its solution

On the blow-up of solutions to the periodic modified integrable Camassa--Holm equation

Min Zhu^1, and
Shuanghu Zhang^2,

1.
Department of Mathematics, Nanjing Forestry University, Nanjing 210036
2.
Department of Mathematics, Southwest University, Chongqing 400715

Received: February 28, 2015

Revised: March 31, 2015

Published: May 2017

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Abstract

We derive conditions on the initial data, including cases where the initial momentum density is not of one sign, that produce blow-up of the induced solution to the periodic modified Camassa-Holm equation with cubic nonlinearity. The blow-up conditions and the blow-up rate are formulated in terms of the initial momentum density and the average initial energy.

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Mathematics Subject Classification: 35B44, 35G25.

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