CAJ | 학술논문

利用现代数学理论对具有幂律速度的无限延伸平板边界层问题进行了研究。通过引入适当的相似变换将原边界层方程转化为一类奇异非线性两点边界值问题，利用泛函分析中的控制收敛定理，Schauder不动点定理和近代微分方程理论中的奇异摄动理论和单调逼近技巧，给出了奇异非线性边值问题的负解的存在性和唯一性的严格证明，并给出了无量纲剪切应力和无量纲切向速度的估计公式。
이용현대수학이론대구유멱률속도적무한연신평판변계층문제진행료연구。통과인입괄당적상사변환장원변계층방정전화위일류기이비선성량점변계치문제，이용범함분석중적공제수렴정리，Schauder불동점정리화근대미분방정이론중적기이섭동이론화단조핍근기교，급출료기이비선성변치문제적부해적존재성화유일성적엄격증명，병급출료무량강전절응력화무량강절향속도적고계공식。
Boundary layer problems are studied for boundary conditions corresponding to flow of a infinite stretched surface,which is moving with a power law velocity distribution by using modern mathematical theory. Boundary layer equations are changed into a class of singular nonlinear two-point boundary value problems by introducing appropriate similarity transformation. A rigorous proof for the existence and uniqueness of the negative solutions to the problem by utilizing the dominated convergence theorem and the Schauder fixed theorem in functional analysis and the monotonic approaching technique and singular perturbation theory in the modern theory of differential equations. Estimate formula of dimensionless shear force and dimensionless tangential velocity are obtained.