非线性粘弹性波动方程初边值问题解的爆破
Blow up of the Solution for Initial-Boundary Value Problem of Nonlinear Viscoelastic Wave Equation
摘要
研究一类非线性粘弹性波动方程的初边值问题,证明了该定解问题解的存在性及解在有限时间内爆破.
The initial-boundary value problem of nonlinear viscoelastic wave equation is studied in this paper. The existence of the solution and the blow-up with finite time of the solution are obtained.
出处
《曲阜师范大学学报（自然科学版）》
CAS
2010年第1期13-18,共6页
Journal of Qufu Normal University(Natural Science)
基金
山东省自然科学基金(Q2008A08)
山东省高等学校科技计划项目基金(J09LA04)
曲阜师范大学科研基金(xj0711)
参考文献10
-
1Adams R A. Sobolev Spaces [M]. New York: Academic Press, 1975, 112 -116.
-
2Li Fushan, Bai Yuzhen. Uniform Rates of Decay for Nonlinear Viscoelastic Marguerre - yon Karman Shallow Shell System, [ J]. J Math Anal Appl, 2009, 351 : 522-535.
-
3Li Fushan. Existence and uniqueness of the solution to the the viscoelastic equations for Koiter shells [ J ]. Appl Math Comput, 2008, 200: 407-412.
-
4Cavalcanti M M, Oquendo H P. Frictional versus viscoelastic damping in a semilinear wave equation [ J ]. SIAM J Control Optim, 2003, 42(4) : 1310-1324.
-
5Cavalcanti M M, Domingos Cavalcanti V N, Soriano J A. Exponential decay for the solution of semilinear viscoelastic wave equations with localized damping [ J ]. Electron J Differential Equations, 2002, 44 : 1-14.
-
6Salim A. Messaoudi, General decay of the solution energy in a viscoelastic equation with a nonlinear source[ J ]. Nonlinear Analysis, 2008, 69(8): 2589-2598.
-
7Mohammad Kafini, Salim A Messaoudi. A blow up result in a Cauchy viscoelastic problem[ J]. Applied Math Letters, 2008, 21 : 549-553.
-
8Yong Zhou. A blow - up result for a nonlinear wave equation with damping and vanishing initial energy in R^n[J]. Applied Mathematics Letters, 2005, 18:281-286.
-
9Jong Yeoul Park, Sun Hye Park. Existence and asymptotic stability for viscoelastic problems with nonlocal boundary dissipation [ J ]. Czechoslovak Mathematical Journal, 2006, 56 ( 131 ) : 273-286.
-
10李傅山,孔翠翠.热传导方程的基本解与正态分布密度函数[J].曲阜师范大学学报（自然科学版）,2006,32(3):15-18. 被引量：3
二级参考文献3
-
1王培合,李英.具有积分Ricci曲率界的流形上的Sobolev不等式(英文)[J].曲阜师范大学学报（自然科学版）,2006,32(2):1-5. 被引量：1
-
2复旦大学.概率论基础[M].北京:人民教育出版社,1979..
-
3Evans L C.Partial differential equations[M].Rhode Island:American Mathematical Society Providence,1997.
-
1张宏伟,呼青英.具时滞和记忆项的非线性粘弹性波动方程解的爆破——纪念阳名珠先生[J].应用泛函分析学报,2017,19(1):71-79. 被引量：2
-
2毛凤梅,罗娟,王俊俊.非线性粘弹性波动方程的非协调混合元超收敛分析和外推[J].数学的实践与认识,2015,45(9):205-218.
-
3赵翠玲,李傅山.具有摩擦和记忆性的非线性波动方程一致能量衰减估计(英文)[J].曲阜师范大学学报（自然科学版）,2013,39(2):33-42.
