ON ILL-POSEDNESS FOR THE GENERALIZED BBM EQUATION

被引：10
|
作者：
Carvajal, Xavier [1 ]
Panthee, Mahendra [2 ]
机构：
[1] Inst Matemat UFRJ, Ctr Tecnol, BR-21941972 Rio De Janeiro, RJ, Brazil
[2] Univ Estadual Campinas, UNICAMP, Dept Matemat, BR-13083859 Campinas, SP, Brazil
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2014年 / 34卷 / 11期
基金：
巴西圣保罗研究基金会;
关键词：
Initial value problem; BBM equation; well-posedness; ill-posedness; LOW REGULARITY; BURGERS EQUATION; WELL-POSEDNESS; BENJAMIN-ONO; ISSUES; WAVES;
D O I：
10.3934/dcds.2014.34.4565
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the Cauchy problem associated to the generalized Benjamin-Bona-Mahony (BBM) equation for given data in the L-2-based Sobolev spaces. Depending on the order of nonlinearity and dispersion, we prove that the Cauchy problem is ill-posed for data with lower order Sobolev regularity. We also prove that, in certain range of the Sobolev regularity, even if the solution exists globally in time, it fails to be smooth.
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页码：4565 / 4576
页数：12
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