Asymptotics of the Solution to a Stationary Piecewise-Smooth Reaction-Diffusion-Advection Equation  

作　　者：Qian YANG Mingkang NI 

机构地区：[1]College of Science,University of Shanghai for Science and Technology,Shanghai 200093,China [2]School of Mathematical Sciences,East China Normal University,Shanghai 200062,China [3]Shanghai Key Laboratory of Pure Mathematics and Mathematical Practice,Shanghai 200241,China

出　　处：《Chinese Annals of Mathematics,Series B》2023年第1期81-98,共18页数学年刊（B辑英文版）

基　　金：supported by the National Natural Science Foundation of China (No. 11871217);the Science and Technology Commission of Shanghai Municipality (No. 18dz2271000)

摘　　要：A singularly perturbed boundary value problem for a piecewise-smooth nonlinear stationary equation of reaction-diffusion-advection type is studied.A new class of problems in the case when the discontinuous curve which separates the domain is monotone with respect to the time variable is considered.The existence of a smooth solution with an internal layer appearing in the neighborhood of some point on the discontinuous curve is studied.An efficient algorithm for constructing the point itself and an asymptotic representation of arbitrary-order accuracy to the solution is proposed.For sufficiently small parameter values,the existence theorem is proved by the technique of matching asymptotic expansions.An example is given to show the effectiveness of their method.

关 键 词：Reaction-Diffusion-Advection equation Internal layer Asymptotic method Piecewise-Smooth dynamical system 

分 类 号：O175[理学—数学]