This paper is concerned with the asymptotic profiles of positive solutions for diffusive logistic equations. The aim is to study the sharp effect of nonlinear diffusion functions. Both the classical reaction–diffusion equation and nonlocal dispersal equation are investigated. We prove the sharp change occurs in reaction–diffusion equation by regularity estimates and compact principle. Due to lack of compactness and regularities theory for nonlocal problems, we obtain the sharp changes by nonlocal estimates and comparison arguments. Our result reveals the nonlinear term plays quite different roles between evolution problem and stationary solution problem.

中文翻译：

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扩散逻辑方程中的渐近剖面

本文关注的是扩散逻辑方程正解的渐近分布。目的是研究非线性扩散函数的尖锐效应。研究了经典的反应扩散方程和非局部扩散方程。我们通过正则性估计和紧致原理证明了反应-扩散方程发生了急剧变化。由于缺乏非局部问题的紧凑性和规律性理论，我们通过非局部估计和比较论证获得了急剧变化。我们的结果表明非线性项在进化问题和平稳解问题之间扮演着截然不同的角色。