GEOMETRIC APPROACH TO BOUNDARY-LAYER PROBLEMS EXHIBITING RESONANCE

被引:23
作者
KOPELL, N
机构
关键词
D O I
10.1137/0137035
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
The boundary value problem is considered for the singularly perturbed equation epsilon y double prime plus f(x, epsilon )y prime plus g(x, epsilon )y equals 0 under the assumption that f changes sign and f//x less than 0. It is shown that this problem can be understood by imbedding the equation in a two parameter family epsilon y double prime plus f(x, epsilon , delta )y prime plus g(x, epsilon , delta )y equals 0. Under a transversality condition on f and g, delta equals delta ( epsilon ) is computed so that the latter equation displays resonance. The same techniques are used to show that B. J. Matkowsky's criteria provide a simple and effective way to compute the Taylor series of delta ( epsilon ).
引用
收藏
页码:436 / 458
页数:23
相关论文
共 18 条
[1]  
Abramowitz M., 1964, HDB MATH FUNCTIONS F
[2]  
ACKERBERG RC, 1970, STUD APPL MATH, V49, P277
[3]  
Bender CM., 1978, ADV MATH METHODS SCI
[4]  
Birkhoff G, 1969, ORDINARY DIFFERENTIA
[5]  
COOK LP, 1973, STUD APPL MATH, V52, P129
[6]  
FENICHEL N, 1971, INDIANA U MATH J, V21, P193
[7]  
FENICHEL N, 1978, GEOMETRIC SINGULAR P
[8]  
KOPELL N, 1977, NONLINEAR DIFFUSION
[9]   REMARKS ON SINGULAR PERTURBATIONS WITH TURNING POINTS [J].
KREISS, HO ;
PARTER, SV .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 1974, 5 (02) :230-251
[10]  
LAKIN WD, 1972, STUD APPL MATH, V51, P261