ON ASYMPTOTIC FORMS OF REACTIVE DIFFUSIVE RUNAWAY

被引:7
作者
DOLD, JW
机构
来源
PROCEEDINGS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES | 1991年 / 433卷 / 1889期
关键词
D O I
10.1098/rspa.1991.0063
中图分类号
O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];
学科分类号
07 ; 0710 ; 09 ;
摘要
Different aspects of reactive-diffusive runaway are discussed in this paper. It is shown that a wide range of reactive nonlinearities can be analysed in essentially the same way, leading to the conclusion that there appear to be only two distinct non-singular, self-similar or approximately self-similar forms of description for non-homogeneous blowup. These exactly self-similar and asymptotically self-similar descriptions have previously been recognized, but are examined here in some detail for many different types of nonlinearity using asymptotic and numerical techniques. It is confirmed that exactly self-similar descriptions only behave non-pathologically in fairly extreme, discrete cases that are very close to a reactive-diffusive (or steady-state) balance under three or more dimensions of symmetry. Quantitative identification of these cases indicates that they may be of dubious practical relevance. It is then shown that only one class of non-singular, asymptotically self-similar descriptions can be found using coordinate perturbation techniques. Resulting solutions are derived to a high asymptotic order and are found to reveal a fairly universal structure for symmetric blowup. A simple analysis reveals that non-symmetric blowup also fits in with this structure, at least to leading order.
引用
收藏
页码:521 / 545
页数:25
相关论文
共 25 条
[1]  
Barenblatt G, 1979, SIMILARITY SELF SIMI
[2]   NONEXISTENCE FOR THE KASSOY PROBLEM [J].
BEBERNES, J ;
TROY, W .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1987, 18 (04) :1157-1162
[3]  
BEBERNES J, 1988, MATH MODELLING COMBU, P383
[4]  
Bebernes J., 1989, MATH PROBLEMS COMBUS, V83
[5]  
BRESSAN A, 1991, IN PRESS J DIFFL EQU
[6]   ANALYSIS OF THERMAL RUNAWAY IN THE IGNITION PROCESS [J].
DOLD, JW .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1989, 49 (02) :459-480
[7]   ANALYSIS OF THE EARLY STAGE OF THERMAL RUNAWAY [J].
DOLD, JW .
QUARTERLY JOURNAL OF MECHANICS AND APPLIED MATHEMATICS, 1985, 38 (AUG) :361-387
[8]  
DOLD JW, 1988, MATH MODELLING COMBU, P461
[10]   EXISTENCE OF LOGARITHMIC-TYPE SOLUTIONS TO THE KAPILA-KASSOY PROBLEM IN DIMENSIONS 3 THROUGH 9 [J].
EBERLY, D ;
TROY, WC .
JOURNAL OF DIFFERENTIAL EQUATIONS, 1987, 70 (03) :309-324