论文标题
退化扩散转化反应方程的波前与标志变化的扩散率
Wavefronts for degenerate diffusion-convection reaction equations with sign-changing diffusivity
论文作者
论文摘要
我们在本文中考虑了一个空间维度的扩散转化反应方程。主要的假设是关于一个单一的反应项，而扩散率是一两次变化的扩散率。然后，我们处理一个前向抛物线方程。我们的主要结果涉及全球定义的行进波的存在，它们连接了两个均衡并跨越两个区域，在两个区域中，扩散率为正，而区域为负。我们还研究了轮廓的单调，并在扩散率退化的点上显示了尖锐行为的出现。特别是，如果这样的点是内部点，那么敏锐的行为是新的和不寻常的。
We consider in this paper a diffusion-convection reaction equation in one space dimension. The main assumptions are about the reaction term, which is monostable, and the diffusivity, which changes sign once or twice; then, we deal with a forward-backward parabolic equation. Our main results concern the existence of globally defined traveling waves, which connect two equilibria and cross both regions where the diffusivity is positive and regions where it is negative. We also investigate the monotony of the profiles and show the appearance of sharp behaviours at the points where the diffusivity degenerates. In particular, if such points are interior points, then the sharp behaviours are new and unusual.
