On propagation of regularities and evolution of radius of analyticity in the solution of the fifth-order KdV-BBM model

被引：2
|
作者：
Carvajal, X. [1 ]
Panthee, M. [2 ]
机构：
[1] Univ Fed Rio de Janeiro, Inst Matemat, BR-21941909 Rio de Janeiro, RJ, Brazil
[2] Univ Estadual Campinas, IMECC, BR-13083859 Sao Paulo, SP, Brazil
来源：
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK | 2022年 / 73卷 / 02期
基金：
巴西圣保罗研究基金会;
关键词：
Nonlinear dispersive wave equations; Water wave models; KdV equation; BBM equation; Cauchy problems; Local and global well-posedness; Analyticity; Gevrey class; NONLINEAR DISPERSIVE MEDIA; AMPLITUDE LONG WAVES; DE-VRIES EQUATION; SPATIAL ANALYTICITY; GENERALIZED KORTEWEG; BOUSSINESQ EQUATIONS; WELL-POSEDNESS; RESPECT; SYSTEMS;
D O I：
10.1007/s00033-022-01704-0
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the initial value problem (IVP) associated with a fifth-order KdV-BBM-type model that describes the propagation of unidirectional water waves. We prove that the regularity in the initial data propagates in the solution; in other words, no singularities can appear or disappear in the solution to this model. We also prove the local well-posedness of the IVP in the space of the analytic functions, the so-called Gevrey class. Furthermore, we discuss the evolution of radius of analyticity in such class by providing explicit formulas for upper and lower bounds.
引用
收藏
页数：15
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