论文标题
退化扩散的趋化系统波速的降低机制
A reducing mechanism on wave speed for chemotaxis systems with degenerate diffusion
论文作者
论文摘要
本文与多孔介质类型的退化扩散的趋化模型有关的波动波解决方案。我们建立了半通飞行波的存在，包括锋利的类型和$ c^1 $类型的半限制波。我们的结果表明，趋化性降低了半限定行动波的波速，即用多孔培养基（退化）扩散的趋化波速小于没有趋化性的多孔培养基方程。如我们所知，这是现有文献中未显示的新结果。结果似乎有些令人惊讶，因为趋化性是一种结缔组织。我们通过Schauder的固定点定理证明了我们的结果，并通过各种方法估算了波速。
This paper is concerned with traveling wave solutions for a chemotaxis model with degenerate diffusion of porous medium type. We establish the existence of semi-finite traveling waves, including the sharp type and $C^1$ type semi-finite waves. Our results indicate that chemotaxis slows down the wave speed of semi-finite traveling wave, that is, the traveling wave speed for chemotaxis with porous medium (degenerate) diffusion is smaller than that for the porous medium equation without chemotaxis. As we know, this is a new result not shown in the existing literature. The result appears to be a little surprising since chemotaxis is a connective force. We prove our results by the Schauder's fixed point theorem and estimate the wave speed by a variational approach.
