论文标题
关于包含自我和交叉扩散的反应扩散系统中的模式形成
On pattern formation in reaction-diffusion systems containing self- and cross-diffusion
论文作者
论文摘要
在本文中，我们提出了一个统一的框架，以便使用自由能方法研究包含自我和交叉扩散的反应扩散系统。该框架自然会导致能源法的制定，以及尊重后者离散版本的数值方法。它构成了另一种方法，并补充了标准线性稳定性分析，因为它允许对非线性模式进行数值研究，同时甚至在复杂的几何形状中监测能量演化。作为应用程序，我们提出并研究了一个以自我和交叉扩散术语增强的经过改进的灰色 - 斯科特系统。数值模拟揭示了原始模式，明显不同于仅使用线性扩散获得的原始模式
In this article we propose a unified framework in order to study reaction-diffusion systems containing self- and cross-diffusion using a free energy approach. This framework naturally leads to the formulation of an energy law, and to a numerical method respecting a discrete version of the latter. It constitutes an alternative method and complements the standard linear stability analysis, as it allows for the numerical study of nonlinear patterns, while monitoring the energy evolution, even in complex geometries. As an application, we propose and study a modified Gray-Scott system augmented with self- and cross-diffusion terms. Numerical simulations unveil original patterns, clearly distinct from those obtained with linear diffusion only
