Wave breaking and asymptotic analysis of solutions for a class of weakly dissipative nonlinear wave equations

被引:1
作者
Freire, Igor Leite [1 ,2 ,3 ]
Toffoli, Carlos Eduardo [3 ,4 ]
机构
[1] Silesian Univ Opava, Math Inst, Na Rybnicku 1, Opava 74601, Czech Republic
[2] Univ Fed Sao Carlos, Dept Matemat, Rodovia Washington Luis,Km 235, BR-13565905 Sao Carlos, SP, Brazil
[3] Univ Fed ABC, Programa Posgrad Matemat, Ave Estados 5001, BR-09210580 Santo Andre, SP, Brazil
[4] Inst Fed Educ Ciencia & Tecnol Sao Paulo, Campus Campos Jordao,Rua Monsenhor Jose Vita 280, BR-12460000 Abernessia, SP, Brazil
基金
瑞典研究理事会; 巴西圣保罗研究基金会;
关键词
Wave breaking of solutions; Conserved quantities; Persistence properties; Asymptotic profiles; SHALLOW-WATER EQUATION; CAMASSA-HOLM EQUATION; UNIQUE CONTINUATION; WELL-POSEDNESS; CAUCHY-PROBLEM; PERSISTENCE; EXISTENCE;
D O I
10.1016/j.jde.2023.02.011
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study formation of singularities and persistence properties of solutions for a class of non-local and non-linear evolution equations with an arbitrary function and a non-negative (dissipation) parameter, which includes the famous Camassa-Holm equation and other recently reported hydrodynamic models as particular members. In case such a parameter is positive, solutions emanating from Cauchy problems have time decaying norms bounded from above by the norm of the corresponding initial datum. Whenever the function is even, for a given odd initial datum with slope satisfying a certain relation involving the dissipation parameter, then the corresponding solution of the problem breaks at finite time. We can also describe scenarios for the occurrence of wave breaking for more general initial data or functions, provided that those latter satisfy certain conditions on their first derivatives. We also study asymptotic behavior and unique continuation properties for solutions of the equation. (c) 2023 Elsevier Inc. All rights reserved.
引用
收藏
页码:457 / 483
页数:27
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