This paper is concerned with the existence of entire solutions for a reaction-diffusion equation with doubly degenerate nonlinearity. Here the entire solutions are the classical solutions that exist for all [Formula: see text]. With the aid of the comparison theorem and the sup-sub solutions method, we construct some entire solutions that behave as two opposite traveling front solutions with critical speeds moving towards each other from both sides of x-axis and then annihilating. In addition, we apply the existence theorem to a specially doubly degenerate case.

中文翻译：

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具有双简并非线性的反应扩散方程的整体解。

本文关注具有双简并非线性的反应扩散方程的整体解的存在。在这里，整个解决方案是所有[公式：请参见文本]都存在的经典解决方案。借助于比较定理和sup-sub解法，我们构造了一些完整的解，它们表现为两个相对的行进前解，其临界速度从x轴的两侧移向彼此，然后then没。另外，我们将存在性定理应用于一个特殊的双重退化情形。