混合边值双相延迟非Fourier温度场的奇摄动解  

Singularly perturbed solution of mixed boundary value two-phase delayed non-Fourier temperature field

作　　者：蒋亚楠 包立平[1] 吴立群[2] 陈序 JIANG Yanan;BAO Liping;WU Liqun;CHEN Xu(School of Sciences,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China;School of Mechanical Engineering,Hangzhou Dianzi University,Hangzhou Zhejiang 310018,China)

机构地区：[1]杭州电子科技大学理学院,浙江杭州310018 [2]杭州电子科技大学机械工程学院,浙江杭州310018

出　　处：《杭州电子科技大学学报（自然科学版）》2023年第4期76-82,共7页Journal of Hangzhou Dianzi University：Natural Sciences

基　　金：国家自然科学基金资助项目(51775154)。

摘　　要：研究一类特殊的双相延迟非Fourier热传导模型,得到具有混合非齐次边值条件的混合方程,并用奇异摄动方法求解该方程。首先,采用正则摄动展开得到抛物方程,用分离变量法求得外解,并进行初始层矫正;然后,分别对2个角域进行矫正,运用拉普拉斯变换法求解,从而确定该方程渐近解的展开式;最后,对混合方程渐近解做余项估计,证明了渐近解在L 2意义下的一致有效性。In this paper,a special dual-phase-lag non-Fourier heat conduction model is studied,and a mixed equation with mixed inhomogeneous boundary value conditions is obtained.We solve the equation with the singular perturbation method,by using the canonical perturbation expansion to obtain the parabolic equation,using the separation variable method to obtain the outer solution,carrying out the initial layer correction,and then respectively correcting the two angles.The domain is corrected and solved by the Laplace transform method to determine the expansion of the asymptotic solution of the equation.Finally,the remainder of its asymptotic solution is estimated,which proves the uniform validity of the asymptotic solution in the sense of L 2.

关 键 词：奇摄动 双相延迟热传导 混合边值问题 一致有效性 

分 类 号：O175.2[理学—数学]