吉林大学学报（理学版）2025，Vol.63Issue(4)：993-1004,12.DOI:10.13413/j.cnki.jdxblxb.2024408
一类二维奇摄动反应扩散方程空间对照结构型解
Spatial Contrastive Structural Solutions in a Class of Two-Dimensional Singularly Perturbed Reaction-Diffusion Equations
摘要
Abstract
We considered a class of two-dimensional singularly perturbed reaction-diffusion problems with discontinuous reaction terms.Firstly,using spatial contrastive structural theory,boundary layer function methods,smooth seaming method,and asymptotic differential inequality methods,we constructed asymptotic expansion of the problem with solutions for the internal layer and boundary layer up to the n order,where n was an arbitary constant.Secondly,we proved the existence and local asymptotic stability of the solution with internal layer,and constructed high-precision asymptotic expansion of the solution.Finally,we applied the obtained theoretical results to a numerical example.关键词
奇异摄动/反应扩散方程/空间对照结构理论/渐近展开式Key words
singular perturbation/reaction-diffusion equation/spatial contrastive structural theory/asymptotic expansion分类
数理科学引用本文复制引用
吴潇,郄佳音,谢峰..一类二维奇摄动反应扩散方程空间对照结构型解[J].吉林大学学报（理学版）,2025,63(4):993-1004,12.基金项目
国家自然科学基金面上项目(批准号:12271088)、上海市自然科学基金面上项目(批准号:21ZR1401000)和中央高校基本科研业务费专项基金(批准号:2232023D-22). （批准号:12271088）
