具阻尼的高维广义Boussinesq 方程的Cauchy 问题的整体适定性

数学物理学报 ›› 2014, Vol. 34 ›› Issue (5): 1173-1187.

具阻尼的高维广义Boussinesq 方程的Cauchy 问题的整体适定性

沈继红^1,2, 张明有¹, 杨延冰¹, 刘博为², 徐润章²

1.哈尔滨工程大学自动化学院哈尔滨 150001|
2.哈尔滨工程大学理学院哈尔滨 150001

收稿日期:2013-10-08 修回日期:2014-04-06 出版日期:2014-10-25 发布日期:2014-10-25
基金资助:
国家自然科学基金(11101102)、高等学校博士学科点专项科研基金(20102304120022)、黑龙江省博士后基金、黑龙江省普通高等学校青年学术骨干支持项目(1252G020)和中央高校基本科研业务费专项资金资助

Global Well-posedness of Cauchy Problem for Damped Multidimensional Generalized Boussinesq Equations

SHEN Ji-Hong^1,2, ZHANG Ming-You¹, YANG Yan-Bing¹, LIU Bo-Wei², XU Run-Zhang²

1.College of Automation, Harbin Engineering University, |Harbin 150001;\
2. College of Science, Harbin Engineering University, Harbin 150001

Received:2013-10-08 Revised:2014-04-06 Online:2014-10-25 Published:2014-10-25
Supported by:
国家自然科学基金(11101102)、高等学校博士学科点专项科研基金(20102304120022)、黑龙江省博士后基金、黑龙江省普通高等学校青年学术骨干支持项目(1252G020)和中央高校基本科研业务费专项资金资助

摘要/Abstract

摘要：

研究了一类具阻尼的高维广义Boussinesq 方程u_tt-Δu-Δu_tt+Δ²u- kΔu_t=Δf(u) 的Cauchy 问题. 在没有建立问题局部解存在性理论的情况下,利用位势井方法分析了阻尼系数k与初值及井深之间的关系, 得到了整体解存在与不存在的门槛结果.

关键词: 具阻尼的高维广义Boussinesq 方程, Cauchy 问题, 整体存在性, 不存在性, 位势井方法

Abstract:

We study the Cauchy problem for a class of damped multidimensional generalized Boussinesq equations u_tt-Δu-Δu_tt+Δ²u- kΔu_t=Δf(u), where k>0. By using potential well method, we analyze the relation between the coefficient k of damping term and the initial data as well as the depth of potential well and obtain the existence and nonexistence of global
weak solution without establishing the local existence theory.

Key words: Damped multidimensional generalized Boussinesq equations, Cauchy problem, Global existence, Nonexistence, Potential well method

中图分类号:

35L75

沈继红, 张明有, 杨延冰, 刘博为, 徐润章. 具阻尼的高维广义Boussinesq 方程的Cauchy 问题的整体适定性[J]. 数学物理学报, 2014, 34(5): 1173-1187.

SHEN Ji-Hong, ZHANG Ming-You, YANG Yan-Bing, LIU Bo-Wei, XU Run-Zhang. Global Well-posedness of Cauchy Problem for Damped Multidimensional Generalized Boussinesq Equations[J]. Acta mathematica scientia,Series A, 2014, 34(5): 1173-1187.

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