应用数学进展  >> Vol. 4 No. 1 (February 2015)

一类高阶n维非线性发展方程组的初边值问题
The Initial Boundary Value Problems for a Class of n-Dimensional Nonlinear Evolution Systems of Higher Order

DOI: 10.12677/AAM.2015.41003, PDF, HTML, XML, 下载: 2,319  浏览: 6,484 

作者: 刘 杰, 肖黎明:广东技术师范学院计算机科学学院,广东 广州

关键词: 非线性波动方程组先验估计Galerkin方法Sobolev嵌入定理整体强解Nonlinear Wave System Prior Estimate Galerkin Method Sobolev Embedding Theorem The Global Strong Solution

摘要: 本文研究了一类高阶n维非线性波动方程组,通过解的先验估计,利用Galerkin方法和Sobolev嵌入定理,证明了初边值问题整体强解的存在性和唯一性。
Abstract: In this paper, we study a class of n-dimensional nonlinear wave system of high order by using the Galerkin method, Sobolev embedding theorem and prior estimate of solution, and prove the exis-tence and uniqueness of global strong solution to the initial boundary value problem.

文章引用: 刘杰, 肖黎明. 一类高阶n维非线性发展方程组的初边值问题[J]. 应用数学进展, 2015, 4(1): 15-28. http://dx.doi.org/10.12677/AAM.2015.41003