一类非线性强阻尼的Sine-Gordon型方程的初边值问题  

The Initial Boundary Value Problem for a Kind of Nonlinear Sine-Gordon Equation With Strong Damping

作　　者：段振兴[1] 王颖[1] 

机构地区：[1]太原工业学院,山西太原030008

出　　处：《忻州师范学院学报》2016年第5期6-8,共3页Journal of Xinzhou Teachers University

摘　　要：文章研究了数学中的非线性强阻尼Sine-Gordon型方程,证明了该方程在一定的初边界条件下以及一定的空间下解的存在性。特别在文献[1]的基础上,加了非线性项σ(μ^(1))^(1)和改变了边界条件u(0,t)=0,u^(1)(l,t)=-γu(l,t)。把偏微分方程问题转化为关于ajm(t)的常微分方程组的柯西问题,界定一个变量,利用Galerkin方法,求出了方程的唯一解。we study some researches on a kind of nonlinear and strong damp Sine-Gordon equation of the physics and give the proof of existence and uniqueness under a certain initial boundary conditions and a certain space by Galerkin method. Especially on the basis of the paper [1],the nonlinear term and the boundary conditions are changed. The problem of partial differential equations is transformed into the Cauchy problem of ordinary differential equations,a variable is defined,and the unique solution of the equation is obtained by using the Galerkin method.

关 键 词：非线性 GALERKIN法 弱解 

分 类 号：O175.29[理学—数学]