用钱伟长-Latta方法求非线性扩散过程的渐近解
Asymptotic Solution to a Nonlinear Diffusion Process by Chien-Latta’s Method
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摘要: 本文用钱伟长-Latta[5]的合成展开法,求得了一种非线性扩散过程的方程组的一阶渐近解,简化并改进了前人的工作[4].对于一种特殊情形给出了完整的解析解,并讨论了分叉点上的周期解.所得的结果与实验事实相符.Abstract: In this paper, by using Chien Wei-zang-Latta's composite expansion Method[5], we have obtained the first-order asymptotic solution to a system of equations for a nonlinear diffusion process, therefore, simplifying and improving the previous work[4] considerably. Moreover, a kind of complete analytical solution has been given for a special case, and the periodic solution at the bifurcation point has been discussed, the related result being in agreement with the experiments.
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[1] Hlavacek,V.and H,Hofmann,Chem.Engrg.Sci.,25(1970).1517-1526. [2] Hlavacek,V.,M,K ubicek and J,Jelinek,ibid,25,(1970),1441-1461. [3] Poore,A.B.,Stability and bifurcation phenomena in chemical reactor theory,Ph,D,thesis,California Institute of Technology,Pasadena(1972). [4] Cohen,D,S.,SIAM.J,Appl,Math.,25(1973),640-654. [5] 钱伟长(主编),《奇异摄动理论及其在力学中的应用》,科学出版(1981). [6] Nayfeh,A., H.,Perturbation Methods,John Wiley,New York(1973). [7] Lindburg,R.C,and R.A,Schmitz,Interuot,J.Heat Moss Transfer,14(1971),718-721. [8] 安德罗诺夫.《振动理论》第六章.科学出版社(1973). -
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