源于膨胀波边界层理论中的一类奇异边值问题

Singular Nonlinear Boundary Value Problems Arising in the Boundary Layer Behind Expansion Wave

中文关键词:  膨胀波  边界层  奇异边值问题  存在性和唯一性  正解  壁摩擦  估计式.

英文关键词:expansion wave  boundary layer  singular boundary value problems  existence and uniqueness  positive solution  skin friction  estimation.

中文摘要:

      对源于膨胀波边界层理论中的一类奇异边值问题进行了研究,利用单调逼近方法得到了满足物理意义上正解的存在性和唯一性的充分条件,同时给出了用速度比例参数表示的壁摩擦的估计公式, 利用打靶法技巧得到了问题的数值解.数值结果证明了估计公式的可靠性和有效性.

英文摘要:

      A class of singular nonlinear boundary value problems arising in the boundary layer behind expansion wave are studied. Sufficient conditions for the existence and uniqueness of positive solutions to the problems are established by utilizing the monotonic approaching technique. And a theoretical estimate formula for skin friction coefficient is presented. The numerical solution is presented by using the shoot method. The reliability and efficiency of the theoretical prediction are verified by numerical results.