摘要
多孔介质动力学及生物群体动力学方程引起愈来愈多的人的注意,退化-奇异抛物型方程(u^m/m)_t=(u^k)_(xx)+u^nf(u)的行波解也成为人们关心的课题之一.Aronson对 m=k=1,u^nf(u)∈C^1[0,1]讨论了单调行波解的存在性与正则性,Hosono 对m=1,k≥2,n=0,f∈C^2[0,1],f(0)=f(1)=0,f′(0)<0,f″(0)(?)0,f′(1)<0且在(0,α)内 f(u)<0;在(α,1)内 f(u)>0。
The existence of monotone and non-monotone travelling wave solutions for some degen-erate-singular parabolic equations (u^m/m)_t=(u^k)_(xx)+U^nf(u) is discussed in this paper.Moreo-ver,the regularity of monotone travelling wave solutions is studied.It will be proved that theconclusions of travelling waves for the equation u_t=u_(xx)+u(u-a)(1-u) also hold for themore extensive equations.And we only assume that f(u) is to be continuous.
出处
《系统科学与数学》
CSCD
北大核心
1992年第4期341-349,共9页
Journal of Systems Science and Mathematical Sciences
基金
河南省科委基金
