具有羅賓邊值條件的一類奇攝動微分方程的內(nèi)部層

德米 倪明康

摘要：本文研究了一類具有羅賓邊值條件的二階奇攝動右端不連續(xù)微分方程，用邊界層函數(shù)法構(gòu)造了該類方程解的漸近表達式，最后用縫接法證明了該問題解的存在性，并給出了漸近解的余項估計.

關(guān)鍵詞：奇攝動;漸近表達式;羅賓邊值條件;內(nèi)部層

[參考文獻]

[1]NEFEDOV N N， NI M K. The inner layers in the one-dimensional reaction-diffusion equation with a discontinuous reactive term [J] .Journal of Computational Mathematics and Mathematical Physics， 2015， 55（12） ： 2042-2048.

[2] LEVASHOV N T， NEFEDOV N N. ORLOV A O. Stationary reaction-diffusion equation with a discontinuous reactive term [J].Journal of Computational Mathematics and Mathematical Physics， 2017， 57（5）： 854-866. DOI： 10.1134/S0965542517050062.

[3]VASILYEVA A B， BUTUZOV V F. NEFEDOV N N. Singularly perturbed problems with boundary inner layers EJl . Proceedings of theSteklov Mathematical Institute， Russian Academy of Sciences， 2010， 268： 268-283.

[4]VOLKOV V， NEFEDOV N N. Asymptotic-numerical investigation of generation and motion of fronts in phase transition models [M] //. Numerical Analysis and Its Applications. Berlin： Springer-Verlag， 2012： 524-531.

[5] VASILYEVA A B， BUTUZOV V F. Asymptotic Methods in the Theory of Singular Perturbations [M]. Moscow： Higher School， 1990： 208.