| 摘要: |
| 讨论退化的抛物型方程(um/m)t=(k(u)ux)x+ung(u)的行波解问题.其中n≥0,m >0,g:[0,1]→R+,g(1)=0且存在θ∈(0,1)使得g(u)≡ 0,u∈[0,θ),g(u)>0,u∈(θ,1),g(u)在[θ,1]上Lipschitz连续.证明存在唯一一个正波速的波前解,其中当0 < m < 1时,该波前解为有限行波解,推广了文献[5]的相应结果. |
| 关键词: 退化的抛物型方程 波前解 有限行波解 |
| DOI： |
| 投稿时间：2000-10-30 |
| 基金项目: |
|
| Travelling Wave Solution for a Nonlinear Degenerate Parabolic Equation |
|
Chen Wuhua
|
| (Dept. of Math., Guangxi Univ. for Nationalities, Xixiangtang, Nanning, Guangxi, 530006, China) |
| Abstract: |
| Consider the travelling wave solution problem for the degenerate parabolic equation (um/m)t=(k(u)ux)x+ung(u), where n ≥ 0,m >0,g:[0,1]→R+,g(1)=0 and exists θ∈(0,1) such that g(u)≡ 0,u∈[0,θ),g(u) >0,u∈ (θ,1),g(u) is Lipschitz continuous on[θ,1]. It is proven that there exists a unique travelling wave front solution with positive wave speed and the travelling wave is a finite travelling wave if 0 < m < 1, the corresponding results in Reference are extended. |
| Key words: degenerate parabolic equation travelling wave front solution finite travelling wave solution |
