弱耗散μ-Hunter-Saxton方程的爆破

doi:10.6040/j.issn.1671-9352.0.2014.275

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (05): 55-59.doi: 10.6040/j.issn.1671-9352.0.2014.275

弱耗散μ-Hunter-Saxton方程的爆破

吕红杰, 刘静静, 齐静, 刘硕

郑州轻工业学院数学与信息科学学院, 河南郑州 450002

收稿日期:2014-06-16 出版日期:2015-05-20 发布日期:2015-05-29
通讯作者: 刘静静(1983-),女,博士,讲师,研究方向为非线性色散波方程、p(x)拉普拉斯方程.E-mail:jingjing830306@163.com E-mail:jingjing830306@163.com
作者简介:吕红杰(1977-),女,硕士,讲师,研究方向为非线性偏微分方程.E-mail:lhjsjf@163.com
基金资助:
国家自然科学基金数学天元基金资助项目(11326161);河南省教育厅科学技术研究重点资助项目(14A110011,12B110029);郑州轻工业学院博士基金资助项目(2013BSJJ052)

Blow-up of a weakly dissipative μ-Hunter-Saxton equation

LÜ Hong-jie, LIU Jing-jing, QI Jing, LIU Shuo

Department of Mathematics and Information Science, Zhengzhou University of Light Industry, Zhengzhou 450002, Henan, China

Received:2014-06-16 Online:2015-05-20 Published:2015-05-29

摘要/Abstract

摘要： 研究了弱耗散μ-Hunter-Saxton方程Caucly问题的爆破现象。给出了一个新的爆破结果,推导出爆破强解精确的爆破率。

关键词: -Hunter-Saxton方程, 爆破, 强解, 弱耗散&mu

Abstract: We study the Cauchy problem of the weakly dissipative μ-Hunter-Saxton equation. The present work is mainly concerned with blow-up phenomena of the equation. We first present a new blow-up result for strong solutions to the equation. Then, we drive the precise blow-up rate for strong solutions to the equation.

Key words: blow-up, strong solution, a weakly dissipative μ-Hunter-Saxton equation

中图分类号:

O175.29

引用本文

吕红杰, 刘静静, 齐静, 刘硕. 弱耗散μ-Hunter-Saxton方程的爆破[J]. 山东大学学报（理学版）, 2015, 50(05): 55-59.

LÜ Hong-jie, LIU Jing-jing, QI Jing, LIU Shuo. Blow-up of a weakly dissipative μ-Hunter-Saxton equation[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(05): 55-59.

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[1]	董莉. 两类非线性波动方程解的爆破时间的下确界[J]. 山东大学学报（理学版）, 2017, 52(4): 56-60.
[2]	刘洋,达朝究,李富明. Nehari流形在一类半线性抛物方程爆破中的应用[J]. 山东大学学报（理学版）, 2016, 51(1): 123-127.
[3]	林春进1,徐国静2. 高维Kaniadakis-Quarati 方程的有限时间爆破[J]. 山东大学学报（理学版）, 2014, 49(06): 79-84.
[4]	宋丹丹,原保全*. 可压缩磁流体方程组的显式爆破解[J]. J4, 2012, 47(2): 26-30.
[5]	代丽美. 完全非线性一致椭圆方程的边界爆破问题[J]. J4, 2011, 46(6): 34-36.
[6]	阎小丽,原保全*. 欧拉方程的显式爆破解[J]. J4, 2011, 46(12): 104-107.
[7]	李凤萍. 三维广义磁流体方程组解的爆破准则[J]. J4, 2010, 45(4): 90-94.
[8]	陆求赐1,曾有栋2. 非局部波动方程组解的半无界问题[J]. J4, 2010, 45(10): 104-108.

弱耗散μ-Hunter-Saxton方程的爆破

Blow-up of a weakly dissipative μ-Hunter-Saxton equation

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