摘要
讨论了一类半线性奇摄动边值问题,构造了问题的具有代数型特点的左右边界层函数和内部角层函数,利用微分不等式理论证明了问题解的存在性,得到了解的渐近估计,给出了该类问题的一般性结论.并且将结论应用于一类燃烧问题的模型,得到了该模型的渐近估计.对有关文献的相关问题及其结果都作了相应的推广.
In this paper, a class of semi-linear singularly perturbed boundary value problems is considered. The left and the right boundary layer functions and the internal corner layer function with algebraic type characteristic are constructed. Using the theory of differential inequalities, the existence of solution for the problem is proved and the asymptotic estimation of solution is obtained. The general conclusion of this problem is given. And the result is applied to a model of combustion problem and the corresponding asymptotic estimation is obtained. The related problem and the corresponding result are generalized.
出处
《系统科学与数学》
CSCD
北大核心
2013年第7期834-840,共7页
Journal of Systems Science and Mathematical Sciences
基金
国家自然科学基金(11071205
10902076)
浙江省自然科学基金(Y13A010005
Y6110502)资助课题
关键词
奇摄动
半线性
微分不等式
渐近估计
Singular perturbation, semi-linear, differential inequalities, asymptotic estimation.
