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一类强阻尼波方程解的存在性和爆破性 被引量：2

Existence and blow-up for a class of strongly damped wave equations
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摘要 讨论一类强阻尼波方程解的局部存在性,并利用势井理论研究解的整体存在性和爆破性. In this paper the local existence of solutions for a class of strongly damped wave equations is considered, and the global existence and blow-up of solutions based on the potential well theory is studied.
作者 徐江
机构地区 浙江大学数学系
出处 《高校应用数学学报（A辑）》 CSCD 北大核心 2006年第2期157-164,共8页 Applied Mathematics A Journal of Chinese Universities(Ser.A)
关键词 强阻尼波方程 存在性 爆破性 strongly damped wave equation existence blow-up
分类号 O175 [理学—基础数学]
  • 相关文献

参考文献5

  • 1Georgiev V,Todorova G.Existence of a solution of the wave equation with nonlinear damping and source terms[J].J Differential Equations,1994,109:295-308.
  • 2Ono K.Global existence,decay,and blow up of solutions for some mildly degenerate nonlinear[J].J Differential Equations,1998,150:203-214.
  • 3Vitillaro E.A potential well theory foy the wave equation with nonlinear source and boundary damping terms[J].Glasgow Math J,2002,44:375-395.
  • 4Barbu V.Nonlinear Semigroups and Differential Equations in Banach Space[M].Amsterdam:Nordhoff,1976.
  • 5Levine H.Instability and nonexistence of global solutions to nonlinear wave equations of the from Putt =-Au + F(u)[J].Trans Amer Math Soc,1974,192:1-21.

同被引文献16

  • 1刘亚成,王锋,刘大成.任意维数的强阻尼非线性波动方程(Ⅰ)——初边值问题[J].应用数学,1995,8(3):262-266. 被引量：14
  • 2方道元,徐江.强阻尼波方程解的整体存在性和一致衰减性[J].数学物理学报（A辑）,2006,26(5):753-765. 被引量：2
  • 3Lions J L. Quelques Methodes de Resolution des Problemes aux Limites non Lineaires. Paris: Dunod-Gauthier Villars, 1969
  • 4Webb G F. Existence and asymptotic behavior for a strongly damped nonlinear wave equation. Canad J Math, 1980, 32:631-643
  • 5Vitillaro E. A potential well theory for the wave equation with nonlinear source and boundary damping terms. Glasgow Math J, 2002, 44:375-395
  • 6Ono K. Global existence, decay and blow up of solutions for some mildly degenerate nonlinear Kirchnoff strings. J Differential Equations, 1997, 137:273-301
  • 7Ma T F, Soriano J A. On weak solutions for an evolution equation with exponential nonlinearities. Nonlinear Anal T M A, 1999, 37:1029-1038
  • 8Yang Zhijian. Existence and asymptotic behaviour of solutions for a class of quasilinear evolution equations with nonlinear damping and source terms. Math Meth Appl Sci, 2002, 25:795-814
  • 9Yang Zhijian, Chen Guowang. Global existence of solutions for quasi-linear wave equations with viscous damping. J Math Anal Appl, 2003, 285:604-618
  • 10Komornik V, Zuazua E. A direct method for boundary stabilization of the wave equation. J Math Pures Appl, 1990, 69:33-54

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高校应用数学学报（A辑）
2006年 第2期

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