具有弱阻尼项的广义IMBq方程初值问题解的整体存在性

数学物理学报 ›› 2015, Vol. 35 ›› Issue (1): 68-82.

具有弱阻尼项的广义IMBq方程初值问题解的整体存在性

陈翔英

郑州电力高等专科学校经济贸易系郑州 450000

收稿日期:2013-06-21 修回日期:2014-06-25 出版日期:2015-02-25 发布日期:2015-02-25
基金资助:
国家自然科学基金(11271336)

Global Existence of Solution of Cauchy Problem for A Generalized IMBq Equation with Weak Damping

CHEN Xiang-Ying

Department of Economy and Trade, Zhengzhou Electric Power College, Zhengzhou 450000

Received:2013-06-21 Revised:2014-06-25 Online:2015-02-25 Published:2015-02-25

摘要/Abstract

摘要：

证明具有弱阻尼项的广义IMBq 方程 $\100dpi \inline $u_{tt}-u_{xx}- u_{xxtt}+\nu_0u_{t}=f(u)_{xx},$ $ x\in {{\Bbb R}},$ $ t>0$$ 的初值问题在

$\100dpi \inline $C^{2}([0,\infty);H^{s}({{\Bbb R}}))$ ($s\geq 2$是一实数)$ 中存在惟一整体广义解和在 $\100dpi \inline $C^{2}([0,\infty);H^{s}({{\Bbb R}}))$ ($s>\frac{7}{2}$)$ 中存在惟一整体古典解,
并给出上述初值问题解爆破的充分条件.

关键词: 具有弱阻尼项的广义IMBq 方程 , 初值问题;整体解 , 解的爆破

Abstract:

In this paper, we prove that the Cauchy problem for the generalized IMBq equations with weak damping, $\100dpi \inline $u_{tt}-u_{xx}-u_{xxtt}+\nu_0u_t=f(u)_{xx}$$ , $\100dpi \inline $x\in {\Bbb R}$,$t>0$$ , admits a unique global generalized solution in $\100dpi \inline $C^2([0,\infty);H^s({{\Bbb R}}))(s\geq 2$$ ~is~real~number) and a unique global classical solution in $\100dpi \inline $C^2([0,\infty);$$H^s({{\Bbb R}}))(s>\frac{7}{2})$$ . We give the sufficient conditionsof the blow up of the solution for the above mentioned Cauchy problem.

Key words: A generalized IMBq equation with weak damping, Cauchy problem , Global solution , Blow up of solution

中图分类号:

35G25

陈翔英. 具有弱阻尼项的广义IMBq方程初值问题解的整体存在性[J]. 数学物理学报, 2015, 35(1): 68-82.

CHEN Xiang-Ying. Global Existence of Solution of Cauchy Problem for A Generalized IMBq Equation with Weak Damping[J]. Acta mathematica scientia,Series A, 2015, 35(1): 68-82.

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