The nonlocal singularly perturbed problem for nonlinear reaction diffusion equation with two parameters
XU Yonghong1, CHEN Xianfeng2, HAN Xianglin3, MO Jiaqi4
(1 Department of Mathematics & Physics, Bengbu College, Bengbu 233030, Anhui, China;2 Department of Mathematics, Shanghai Jiaotong University, Shanghai 200240, China;3 Faculty of Science,Huzhou University, Huzhou 313000, Zhejiang, China;4 Department of Mathematics, Anhui Normal University, Wuhu 241003, Anhui, China)
Abstract:
A class of nonlocal for the singularly perturbed initial boundary value problem of the reaction diffusion equation with two small parameters is considered. Under suitable conditions, the outer solution of the original problem is solved. Using the stretched variables, composing expansion method and expanding theory of power series，the terms of the initial layer and boundary layer are constructed and the formally asymptotic solution is obtained. Finally, using the comparative theorem, the existence of solution for the original problem and the uniformly valid asymptotic expansion are discussed.
KeyWords:
nonlocal; reaction diffusion; singular perturbation
