一类具有无穷边界值的二次奇摄动边值问题  

Second-order quadratic singularly perturbed problems with infinite boundary value

作　　者：韩建邦[1] 沈建和[1] 周哲彦[1] 

机构地区：[1]福建师范大学数学与计算机科学学院,福建福州350007

出　　处：《高校应用数学学报（A辑）》2013年第2期180-188,共9页Applied Mathematics A Journal of Chinese Universities(Ser.A)

基　　金：国家自然科学基金项目(11201072;11102041);福建省教育厅A类项目(JA10065)

摘　　要：研究一类具有无穷边界值的二次奇摄动Robin边值问题解的存在性与解的渐进行为,重点关注边界值的奇异程度对解的边界层行为的影响;同时将所得的结果与Chang及Howes的结果(带正常边界值)进行比较.研究表明:(1)当边界值大小为O(1/ε)时,得到的边界层大小为O(εlnε),这比Chang及Howes带正常边界值的情形提高了O(lnε)量级;(2)增大边界值的奇性至O(1/ε~r),这里r>1,边界层大小的量级不变,依然为O(εlnε);(3)若要使得边界层大小为O(1),则边界值的大小需为O(e^(-1/ε)).最后给出一个算例验证得到的结果.Existence and asymptotic behaviors of solutions in second-order quadratic singularly perturbed problems with infinite boundary value are studied.The paper focuses on the effects of the singularity of boundary value on the behaviors of solutions and the comparisons between the obtained results in this paper and those of Chang and Howes,where the cases with regular boundary values are considered.It is found that：1） when the boundary value is 0（l/ε）, the boundary layer is O（εlnε）.By comparing that of Chang and Howes,the boundary layer has an O（lnε） increase;2） when the boundary value is 0（l/ε~r）,with r1 a constant,the boundary layer is still O（εlnε）;3） to get the 0（1） boundary layer,the boundary value must be 0（e^（-1/ε））.A typical example is performed to verify the obtained results.

关 键 词：二次奇摄动问题 无穷边界值 解的行为 

分 类 号：O175.1[理学—数学]