全部 标题 作者
关键词 摘要

OALib Journal期刊
ISSN: 2333-9721
费用:99美元

查看量下载量

相关文章

更多...
-  2017 

两类非线性波动方程解的爆破时间的下确界
Lower bounds for blow up time of two nonlinear wave equations

DOI: 10.6040/j.issn.1671-9352.0.2016.224

Keywords: 频散项,Petrovsky方程,强阻尼项,爆破,下确界,
dispersive term
,blow-up,Petrovsky equation,strong damping term,lower bound

Full-Text   Cite this paper   Add to My Lib

Abstract:

摘要: 对带有强阻尼项和频散项的非线性黏弹方程和非线性Petrovsky方程的初边值问题进行研究,在方程的解爆破的前提下,通过适当的扰动得到爆破时间的下确界。
Abstract: The initial boundary value problem for the nonlinear viscoelastic euqation with strong damping term and dispersive term and the nonlinear Petrovsky equation is investigated. Under the premise of the solutions blow up of the equations, the lower bound of the blow up time is obtained by the proper perturbation

References

[1]  GEORGIEV V, TODOROVA G. Global existence and blow up of solutions for Cauchy problem of generalized Boussinesq equation[J]. Phys D: Nonlinear Phenomena, 2008, 237:721-731.
[2]  MESSAOUDI S A. Global existence and nonexistence in a system of petrovsky[J]. J Math Anal Appl, 2002, 265: 296-308.
[3]  MESSAOUDI S A. Blow up and global existence in a nonlinear viscoelastic wave equation[J]. Math Nachr, 2003, 260:58-66.
[4]  TAHAMTANI F, SHAHROUZI M. Existence and blow up of ssolutions to a Petrovsky equation with memory and nonlinear source term[J/OL]. Bound Value Probl, 2012, 2012: 50. https://lnk.springer.com/article/10.1186/1687-2770-2012-50.
[5]  LI Fushan, GAO Qingyong. Blow-up of solution for a nonlinear Petrovsky type equation with memoey[J]. Applied Mathematics and Computation, 2016, 274:383-392.
[6]  BERRIMI S, MESSAOUDI S A. Existence and decay of solutions of a viscoelastic equation with a nonlinear source[J].Nonlinear Anal, 2006, 64:2314-2331.
[7]  GAO Qingyong, LI Fushan, WANG Yanguo. Blow-up of the solution for higher-order Kirchhoff-type equations with nonlinear dissipayion[J].Central Eur J Math, 2011, 9(3):686-698.
[8]  KAFINI M, MUSTAFA M I. Blow-up result in a cauchy viscoelastic problem with strong damping and dispersive [J].Nonlinear Analysis: Real World Applications, 2014, 20:14-20.
[9]  GEORGIEV V, TODOROVA G. Existence of solutions of the wave equation with nonlinear damping and source terms[J]. J Differential Equations, 1994, 109:295-308.
[10]  Messaoudi S A. Global existence and nonexistence in s system of Petrovsky equation[J]. Nonlinear Anal, 2009, 70:296-308.
[11]  LIANG Feng, GAO Hongjun. Exponential energy decay and blow-up of solutions for a system of nonlinear Viscoelastic wave equations with strong damping[J].Bound Value Probl, 2011, 1:3-19.
[12]  YANG Zhifeng. Blow-up of solutions for a viscoelastic equation with nonlinear damping[J].Central Eur J Math, 2008, 6(4):568-575.
[13]  PHILIPPIN G A. Lower bounds for blow-up time in a class of nonlinear wave equation[J]. Z Angew Math Phys, 2015, 66:129-134.
[14]  WU Shuntang. General decay of solutions for a viscoelastic equation with nonlinear damping and source terms[J].Acta Math Sci Ser, 2011, 31(4)1436-1448.
[15]  XU Runzhang, YANG Yanbing, LIU Yacheng. Global well-posedness for strongly damped viscoelastic wave equation[J]. Appl Anal, 2013, 92(1):138-157.
[16]  LI Gang, SUN Yun, LIU Wenjun. On asymptotic behavior and blow up of solutions for a nonlinear viscoelastic petrovsky equation with positive initial energy[J]. J Funct Spance Appl, 2013(2103)905867.
[17]  CAVALCANTI M M, CAVALCANTI V N D, FERRIRA J. Existence and uniform decay for nonlinear viscoelastic equation with strong damping[J].Math Methods Appl Sci, 2011, 24:1043-1053.

Full-Text

Contact Us

service@oalib.com

QQ:3279437679

WhatsApp +8615387084133