A class of boundary value problems for the nonlinear nonlocal singularly perturbed fractional differential equation is considered.Firstly,the outer solution of the original problem is obtained.Secondly,by using the st...A class of boundary value problems for the nonlinear nonlocal singularly perturbed fractional differential equation is considered.Firstly,the outer solution of the original problem is obtained.Secondly,by using the stretched variables and the composing expansion method,the shock wave layer and boundary layers are constructed.Finally,by using the theory of differential inequality,the asymptotic behavior of solution for the original boundary value problem of nonlinear nonlocal singularly perturbed fractional differential equation is studied.And the uniformly valid asymptotic estimation is discussed.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(40676016)the Natural Science Foundation of the Education Department of Anhui Province(KJ2015A418)
文摘A class of boundary value problems for the nonlinear nonlocal singularly perturbed fractional differential equation is considered.Firstly,the outer solution of the original problem is obtained.Secondly,by using the stretched variables and the composing expansion method,the shock wave layer and boundary layers are constructed.Finally,by using the theory of differential inequality,the asymptotic behavior of solution for the original boundary value problem of nonlinear nonlocal singularly perturbed fractional differential equation is studied.And the uniformly valid asymptotic estimation is discussed.
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.
