CAJ | 학술논문

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/)时,得到的边界层大小为O( ln ),这比Chang及Howes带正常边界值的情形提高了O(ln )量级;(2)增大边界值的奇性至O(1/ r),这里r >1,边界层大小的量级不变,依然为O( ln );(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/).最后给出一个算例验证得到的结果.
연구일류구유무궁변계치적이차기섭동Robin변치문제해적존재성여해적점진행위,중점관주변계치적기이정도대해적변계층행위적영향;동시장소득적결과여Chang급Howes적결과(대정상변계치)진행비교.연구표명:(1)당변계치대소위O(1/)시,득도적변계층대소위O( ln ),저비Chang급Howes대정상변계치적정형제고료O(ln )량급;(2)증대변계치적기성지O(1/ r),저리r >1,변계층대소적량급불변,의연위O( ln );(3)약요사득변계층대소위O(1),칙변계치적대소수위O(e?1/).최후급출일개산례험증득도적결과.
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 O(1/ ), the boundary layer is O( ln ). By comparing that of Chang and Howes, the boundary layer has an O(ln ) increase; 2) when the boundary value is O(1/ r), with r > 1 a constant, the boundary layer is still O( ln );3) to get the O(1) boundary layer, the boundary value must be O(e?1/ ). A typical example is performed to verify the obtained results.