The singular perturbation problem for reaction diffusion time delay equation with boundary perturbation is considered. Firstly, the outer solution for the initial boundary value problem is constructed. Then, the initi...The singular perturbation problem for reaction diffusion time delay equation with boundary perturbation is considered. Firstly, the outer solution for the initial boundary value problem is constructed. Then, the initial and boundary layer correction terms are obtained using the stretched variables transforms. Finally, the asymptotic behavior of solution for the initial boundary value problem is studied.展开更多
A class of singular perturbation boundary problem of elliptic equation for higher order is studied. Firstly, under suitable conditions, the generalized outer solution to reduced problems is considered. Then the genera...A class of singular perturbation boundary problem of elliptic equation for higher order is studied. Firstly, under suitable conditions, the generalized outer solution to reduced problems is considered. Then the generalized interior shock asymptotic solution to original problem is constructed by using the theory of generalized functions. Finally, using the fixed point theorem of functional analytic, the uniformly validity of the generalized asymptotic solution with interior shock and boundary layers is proved.展开更多
基金Supported by the National Natural Science Foundation of China(11202106)the Natural Science Foundation of the Education Department of Anhui Province(KJ2014A151)the Natural Sciences Foundation from the Universities of Jiangsu Province(13KJB170016)
文摘The singular perturbation problem for reaction diffusion time delay equation with boundary perturbation is considered. Firstly, the outer solution for the initial boundary value problem is constructed. Then, the initial and boundary layer correction terms are obtained using the stretched variables transforms. Finally, the asymptotic behavior of solution for the initial boundary value problem is studied.
基金Supported by the National Natural Science Foundation of China(41275062,11202106)the Natural Science Foundation of the Education Department of Anhui Province(KJ2015A418,KJ2015A347)the Natural Sciences Foundation from the Universities of Jiangsu Province(13KJB170016)
文摘A class of singular perturbation boundary problem of elliptic equation for higher order is studied. Firstly, under suitable conditions, the generalized outer solution to reduced problems is considered. Then the generalized interior shock asymptotic solution to original problem is constructed by using the theory of generalized functions. Finally, using the fixed point theorem of functional analytic, the uniformly validity of the generalized asymptotic solution with interior shock and boundary layers is proved.
