一类退化-奇异抛物型方程的行波解Ⅰ

TRAVELLING WAVE SOLUTIONS FOR SOME DEGENERATE SINGULAR PARABOLIC EQUATIONS I

多孔介质动力学方程吸引了众多人的注意,引起了数学家们的极大兴趣.退化-奇异抛物型方程的行波解也成为令人瞩目的问题.Aronson,Hosono,Atkinson,Engler,Grindron 和 Sleeman,Wang 和 Ye 等在这一领域中都有出色的工作.Aronson 对 m=k=1,u^nf(u)∈C^1[0,1],讨论了单调行波解的存在性.Hosono 对m=1,k≥2,n=0,f∈C^2[0,1],f′(0)<0,f″(0)(?)0,f′(1)<0。

The existence and regularity of travelling wave front solutions are discussed for somedegenerate-singular parabolic equations (u^m/m)_t=u_(xx)+u^(?)f(u).It is proved that theconclusions on wave fronts for the equation u_t=u_(xx)+f(u) also hold for these degenerate-singular equations.Here f(u) is assumed to be continuous.