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具有羅賓邊值條件的一類奇攝動微分方程的內部層

2020-04-10 06:44德米倪明康

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.

關鍵詞:奇攝動;漸近表達式;羅賓邊值條件;內部層

[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.

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