We use a geometric approach to prove the existence of smooth travelling wave solutions of a nonlinear diffusion–reaction equation with logistic kinetics and a convex nonlinear diffusivity function which changes sign twice in our domain of interest. We determine the minimum wave speed, \(c^*\), and investigate its relation to the spectral stability of a desingularised linear operator associated with the travelling wave solutions.

中文翻译：

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负非线性扩散反应模型中的行波解

我们使用一种几何方法来证明存在具有逻辑动力学和凸非线性扩散系数函数的非线性扩散反应方程的光滑行波解的存在，在我们的研究领域，该函数会改变符号两次。我们确定最小波速\（c ^ * \），并研究其与行波解相关的去奇化线性算子的频谱稳定性的关系。