[1]张媛媛,王宏伟.具耗散项非线性发展方程整体解的存在唯一性[J].江西师范大学学报(自然科学版),2014,(01):51-53.
　ZHANG Yuan-yuan,WANG Hong-wei.The Existence and Uniqueness of the Global Solutions for a Class of Nonlinear Evolution Equations with a Dissipative Term[J].Journal of Jiangxi Normal University:Natural Science Edition,2014,(01):51-53.
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具耗散项非线性发展方程整体解的存在唯一性()
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《江西师范大学学报》（自然科学版）[ISSN:1006-6977/CN:61-1281/TN]

卷:
期数:
2014年01期
页码:
51-53
栏目:
出版日期:
2014-02-28

文章信息/Info

Title:
The Existence and Uniqueness of the Global Solutions for a Class of Nonlinear Evolution Equations with a Dissipative Term
作者:
张媛媛;王宏伟
开封大学数学教研部,河南开封,475000；安阳师范学院数学与统计学院,河南安阳,455000
Author(s):
ZHANG Yuan-yuan；WANG Hong-wei
关键词:
耗散项; 整体解; 存在性; 唯一性
Keywords:
dissipative term; global solutions; existence; uniqueness
分类号:
O175.29
文献标志码:
A
摘要:
研究了一类具耗散项非线性发展方程的初边值问题.借助偏微分方程的一些标准技巧对非线性项进行估计,利用嵌入定理和算子半群的方法证明了在相对较弱的条件下上述问题整体解的存在唯一性.
Abstract:
The initial boundary value problem for a class of nonlinear evolution equations with a dissipativeterm was studied.By using some standard methods it was estimated the non-linear term,and by applying embedding theorem and the method of semigroup under rather mild conditions the existence and uniqueness of the global solutions for the above-mentioned problem were obtained.

参考文献/References:

[1] Yang Zhijian.Finite-dimensional attractors for the Kirchhoff equation with a strong dissipation [J].Journal of Mathematical Analysis and Applications,2011,375(2):579-593.
[2] Yang Zhijian.Global attrator for the Kirchhoff type equation with a strong dissipation [J].Differential Equations,2010,249(6):3258-3278.
[3] Chueshov I,Lasiecka I.Long-time behavior of second order evolution equations with nonlinear damping [J].Mem Amer Math Soc,2008,195(3):912-920.
[4] Nakao M.An attractor for a nonlinear dissipative wave equation of Kirchhoff type [J].Math Appl Anal,2009,353(3):652-659.
[5] Gatti S,Pata V,Zelik S.A Gronwall-type lemma with parameter and dissipative estimates for PDEs [J].Nonlinear Anal,2009,70(4):2337-2343.
[6] Filippo Dell'Oro,Vittorino Pata.Strongly damped wave equations with critical nonlinearities [J].Nonlinear Analysis,2012,75(6):5723-5735.
[7] Filippo Dell'Oro,Vittorino Pata.Long-term analysis of strongly damped nonlinear wave equations [J].Nonlinearity,2011,24(4):3413-3435.
[8] Temam R.Infinite dimensional dynamical system in mathematics and physics [M].New York:Springer,1997:100-116.
[9] 姜礼尚,陈亚浙,等.数学物理方程讲义 [M].第2版.北京:高等教育出版社,1996.

备注/Memo

备注/Memo:
国家自然科学基金(10971199)；河南省自然科学基金(092300410067)；河南省教育厅科学技术研究重点课题(13B110137)
更新日期/Last Update: 1900-01-01