一类两参数非线性反应扩散方程奇摄动问题的广义解

发布时间：2019-05-10 13:19

【摘要】：利用奇异摄动方法讨论了一类两参数广义奇摄动反应扩散方程问题.首先,在适当的条件下,对两个小参数进行幂级数展开,构造了问题的形式外部解.其次,在区域边界邻近,建立局部坐标系,利用多重尺度变量方法分别构造了问题解的第一、第二边界层校正项.最后,利用合成展开理论,得到了问题广义解的渐近表示式,并用泛函分析不动点原理,估计了渐近展开式的精度.该文得到问题的广义解在重叠区域内具有两个不同厚度的校正函数.它们分别对边界条件起着校正的作用,扩展了问题研究范围,同时还提供了构造这类在重叠区域上不同厚度的校正项的方法,因此具有广泛的研究前景.
[Abstract]:In this paper, a class of singular perturbed reaction-diffusion equations with two parameters is discussed by using the singular perturbation method. Firstly, under appropriate conditions, the power series expansion of two small parameters is carried out, and the formal external solution of the problem is constructed. Secondly, the local coordinate system is established near the regional boundary, and the first and second boundary layer correction terms of the solution are constructed by using the method of multiple scale variables. Finally, by using the synthetic expansion theory, the asymptotic representation of the generalized solution of the problem is obtained, and the accuracy of the asymptotic expansion is estimated by using the fixed point principle of functional analysis. In this paper, we obtain that the generalized solution of the problem has two correction functions of different thickness in the overlapping region. They play an important role in correcting the boundary conditions, extending the scope of the problem, and also providing a method to construct this kind of correction terms with different thickness in the overlapping region, so they have a wide range of research prospects.
【作者单位】：亳州学院电子与信息工程系;安徽师范大学数学计算机科学学院;
【基金】：国家自然科学基金(11202106) 安徽省教育厅自然科学重点基金(KJ2015A347;KJ2017A702) 安徽省高校优秀青年人才支持计划重点项目(gxyqZ D2016520)~~
【分类号】：O175.29

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