摘要
研究了一类非线性强阻尼广义扰动发展方程问题.它们在数学、力学、物理学等领域中广泛出现.首先,引入一个行波变换,把相应的偏微分方程问题转化为行波方程问题并求出原典型问题的精确解.再用小参数方法和引入伸长变量构造了问题的渐近解.最后,用泛函分析的不动点理论证明了原非线性强阻尼广义扰动发展方程初值问题渐近行波解的存在性,并证明渐近解具有较高的精度和一致有效性.该文求得的渐近解是一个解析展开式,所以它还可继续进行解析运算,而单纯用数值模拟的方法是不行的.
A class of generalized nonlinear strong-damp disturbed evolution differential equations were studied,which widely appeared in the fields of mathematics,mechanics and physics etc.. Firstly,a travelling wave transformation was introduced to convert the related problem of partial differential equations to one of travelling wave equations,with the exact solution to the original typical problem obtained. Then the small parameter method was used and the stretched variables introduced to construct the asymptotic solution. Finally,the existence,high accuracy and uniform validity of the asymptotic travelling wave solution to the original generalized nonlinear strong-damp disturbed evolution equation for the initial-value problem were proved with the fixed point theory for functional analysis. The presented travelling wave asymptotic solution is an analytic expansion,therefore,it is continuously open to analytic operations,which reject the solutions given by those pure numerical methods.
出处
《应用数学和力学》
CSCD
北大核心
2015年第3期315-324,共10页
Applied Mathematics and Mechanics
基金
国家自然科学基金(11202106)~~
关键词
行波
强阻尼
发展方程
travelling w ave
strong damp
evolution equation
