王艳萍.一类具有k阶拉普拉斯算子的波动方程整体解的存在性[J].重庆工商大学自然科学版,2019,36(5):58-62
一类具有k阶拉普拉斯算子的波动方程整体解的存在性
The Existence of Global Solutions for a Class of Wave Equations with k Order Laplace Operators
  
DOI:
中文关键词:  波动方程  整体解  存在性
英文关键词:wave equation  global solutions  existence
基金项目:
作者单位
王艳萍 宿州学院 数学与统计学院安徽 宿州 23400 
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中文摘要:
      针对一类同时含有k阶拉普算子项与多个非线性源项的波动方程的初边值问题,应用Galerkin逼近法证明该方程整体弱解的存在性,这类波动方程改进了含有单个非线性源项的波动方程,由于这类波动方程引入了k阶拉普拉斯算子项和多个非线性源项,使得该波动方程的结构更加精细且符合实际;首先给出了这类波动方程的弱解的定义,然后定义了一些必要的泛函,并利用极限和导数证明了这些泛函所满足的性质以及这类波动方程的解在特定条件下的不变集合;最后应用Galerkin逼近法,借助特征方程的基础解系构造了该波动方程的近似解,通过对近似解收敛性的分析得到了该方程整体弱解的存在性。
英文摘要:
      Aiming at the initial boundary value problem of a class of wave equation with k Laplace operator and multiple nonlinear source terms, Galerkin approximation method is applied to proving the existence of global weak solutions of the equation.This kind of wave equation improves the wave equation with a single non linear source term.Because the wave equation introduces k Laplace operator term and multiple non linear source terms, it makes the structure of the wave equation more refined and practical.Firstly, the definition of weak solutions of the wave equation is given, and then some necessary functionals are defined.The properties of these functionals are proved by using limit and derivative, and the invariant set of solutions of the wave equation under certain conditions is proved.Finally, the Galerkin approximation method is used to construct the approximate solution of the wave equation by means of the basic solution system of the characteristic equation.The existence of the global weak solution of the equation is obtained by analyzing the convergence of the approximate solution.
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