We consider a one-dimensional reaction–diffusion equation of Fisher–Kolmogoroff–Petrovsky–Piscounoff type. We investigate the effect of the interaction between the nonlinear diffusion coefficient and the reaction term on the existence and non-existence of travelling waves. Our diffusion coefficient is allowed to be degenerate or singular at both equilibrium points, 0 and 1, while the reaction term need not be differentiable. These facts influence the existence and qualitative properties of travelling waves in a substantial way.

中文翻译：

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具有非线性退化或奇异扩散的Fisher-KPP方程中的行波

我们考虑Fisher-Kolmogoroff-Petrovsky-Piscounoff型的一维反应扩散方程。我们研究了非线性扩散系数与反应项之间的相互作用对行波的存在与不存在的影响。我们的扩散系数允许在两个平衡点（0和1）处退化或奇异，而反应项不必是可微的。这些事实在很大程度上影响行波的存在和定性。