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一类非线性波动方程的初边值问题 被引量：2

Initial Boundary Value Problem for a Class of Nonlinear Wave Equation
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摘要 利用Galerkin方法结合文中所定义的位势井,证明了一类具有任意耗散项的非线性波动方程存在唯一整体弱解,并在小初始能量的情况下,利用VKomornik不等式证明了整体弱解的渐近性质,推广了相关文献的结论。 This paper studies the initial boundary value problem for a class of nonlinear wave equations with arbitrary dissipative term.The unique and global existence of weak solution is proved by the use of Galerkin and the potential well method.The asymptotic behavior of the weak solution is studied by the V.Komornik inequality in the state of small initial energy.The results show that some related conclusions are improved and generalized.
作者 赵丽英 任俊艳 王周峰
机构地区 河南科技大学理学院
出处 《河南科技大学学报（自然科学版）》 CAS 北大核心 2009年第3期84-87,共4页 Journal of Henan University of Science And Technology:Natural Science
基金 国家自然科学基金项目(10771162) 河南省科技攻关项目(084300510060) 河南省教育厅自然科学基金项目(2006110002)
关键词 非线性波动方程 初边值问题 整体解 解的渐近性质 Nonlinear wave equation Initial boundary problem Global solution Asymptotic behavior of solution
分类号 O175.2 [理学—基础数学]
  • 相关文献

参考文献8

  • 1Yang Zhijian.Global Existence,Asymtotic Behavior and Blowup of Solutions for a Class of Nonlinear Wave Equations With Dissipative Term[J].JDifferential Equations,2003,187:136-155.
  • 2Solange Kouemou Patchev.On Global Solutions and Asymptotic Behaviour for the Generalized Damped Extensible Beam Equation[J].JDifferential Equations,1997,135:299-314.
  • 3Ang D D,Dinh A P N.On the Strongely Damped Wave Equation utt-△u-△ut+f(u)=0[J].SIAM J Math Anal 1998,19:1409-1418.
  • 4杨志坚,陈国旺.具有阻尼项的非线性波动方程的初值问题[J].应用数学学报,2000,23(1):45-54. 被引量：14
  • 5Nakao M,Ono K.Existence of Global Solutions to the Cauchy Problem for the Semilinear Dissipative Wave Equation[J].Math Z,1993,214:325-342.
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  • 8Komornik V.Exact Controllability and Stabilization the Multiplier Method[M].New York:John Wiley,1986.

二级参考文献1

共引文献13

同被引文献15

  • 1Yang Z J. Global Existence, Asymtotic Behavior and Blowup of Solutions for a Class of Nonlinear Wave Equations with Dissipative Term[ J]. J Differential Equations ,2003,187 : 136 - 155.
  • 2Solange K P. On Global Solutions and Asymptotic Behaviour for the Generalized Damped Extensible Beam Equation[ J]. J Differential Equation, 1997,135:299 - 314.
  • 3Chen G W,Yang Z J. Existence and Non-exitence of Globle Solutions for a Class of Nonlinear Wave Equations [ J ]. Math Meth Appl Sci,2000,23:615 - 631.
  • 4Komornik V. Exact Controllability and Stabilization the Muliplier Method[ M ]. New York :John Wiley, 1986.
  • 5MESSAOUDI S A.A note on blow up of solutions of a quasilinear heat equation with vanishing inital enery[J].Journal of mathematical analysis&applications,2002,273(1):243-247.
  • 6LIU W,WANG M.Blow-up of the solutions for a p-Laplacian equtions with positive inital-enery[J].Acta applicandae mathematicae,2008,103(2):141-146.
  • 7TODOROVA G,BITILLARO E.Blow-up for nonlinear dissipative wave equation in RN[J].Journal of mathematical analysis&applications,2005,303(1):242-257.
  • 8MESSAOUDI S A.Blow up and global existence in a nonlinear viscoelastic wave equations[J].Mathematische nachrichten,2003,260(1):58-66.
  • 9MESSOUDI S A.Blow up of positive-initial-energy solutions of a nonlinear viscoelastic hyperbolic equation[J].Journal of mathematical analysis&applications,2006,320(2):902-915.
  • 10LI F,GAO Q.Blow-up of the solutions for a nonlinear Petrovsky type equation with memory[J].Applied mathematics&computation,2016,274(1):383-392.

引证文献2

二级引证文献1

河南科技大学学报（自然科学版）
2009年 第3期

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