We answer three fundamental questions concerning monostable traveling fronts for the scalar Kolmogorov ecological equation with diffusion and spatiotemporal interaction: These are the questions about their existence, uniqueness and geometric shape. In the particular case of the food-limited model, we give a rigorous proof of the existence of a peculiar, yet substantive and nonlinearly determined class of non-monotone and non-oscillating wavefronts.

中文翻译：

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标量Kolmogorov生态方程波前的几何分集

我们回答了三个具有扩散和时空相互作用的标量Kolmogorov生态方程的单稳态行进面的三个基本问题：这是关于它们的存在，唯一性和几何形状的问题。在食物受限模型的特殊情况下，我们给出了一个特殊但实质性和非线性确定的非单调和非振荡波前的存在的严格证明。