Variational approach of critical sharp front speeds in degenerate diffusion model with time delay,Nonlinearity

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Variational approach of critical sharp front speeds in degenerate diffusion model with time delay
Nonlinearity ( IF 1.6 ) Pub Date : 2020-06-15 , DOI: 10.1088/1361-6544/ab801d
Tianyuan Xu _{1,

2} , Shanming Ji ₂ , Ming Mei _{2,

3} , Jingxue Yin ₁

Affiliation

For the classical reaction diffusion equation, the priori speed of fronts is determined exactly in the pioneering paper (R.D. Benguria and M.C. Depassier, {\em Commun. Math. Phys.} 175:221--227, 1996) by variational characterization method. In this paper, we model the dispersal process using a density-dependent diffusion equation with time delay. We show the existence and uniqueness of sharp critical fronts, where the sharp critical front is $C^1$-smooth when the diffusion degeneracy is weaker with $1

中文翻译：

时滞简并扩散模型中临界锐锋速度的变分法

对于经典反应扩散方程，前沿的先验速度在开创性论文（RD Benguria 和 MC Depassier，{\em Commun. Math. Phys.} 175:221--227, 1996）中通过变分表征方法精确确定。在本文中，我们使用具有时间延迟的密度相关扩散方程来模拟扩散过程。我们展示了锐临界前沿的存在性和唯一性，其中锐临界前沿是 $C^1$-smooth 当扩散简并较弱时为 $1

更新日期：2020-06-15

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