一个退化的非线性抛物型方程的行波解

Travelling Wave Solution for a Nonlinear Degenerate Parabolic Equation

关键词:  退化的抛物型方程  波前解  有限行波解

Key words:  degenerate parabolic equation  travelling wave front solution  finite travelling wave solution

摘要:

讨论退化的抛物型方程(u^m/m)t=(k(u)u_x)_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.

Abstract:

Consider the travelling wave solution problem for the degenerate parabolic equation (u^m/m)t=(k(u)u_x)_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.