Mathematical study for pattern formation on localized moving area in reaction-diffusion systems

本文研究了一类反应扩散型系统在有限运动区域内的斑图形成问题。作为这种模式形成的一个例子，Liesegang型降水系统是著名的。众所周知，Liesegang型沉淀的最终图案可能由于凝胶浓度差异或其性质而不同。此外，我们还期望通过对系统的数学理解来控制系统的自组织机制。在这项研究中，我们做了几个模拟与我们提出的模式Liesegang型降水，我们见证了最终模式和外部噪声之间的关系。虽然，当涉及到目标是数学分析的收缩，不幸的是，我们不能得到令人满意的结果，但是，我们想得出结论，有一个未来的发展潜力的基础上，我们从模拟得到的建议。

In this study, we dealt a pattern formation problem which is developed in restricted moving area of reaction-diffusion type system. As an example of such pattern formation, the Liesegang type precipitation system is famous. It is well known that the final patterns of the Liesegang type precipitation may differ due to the gel concentration difference or its nature. Furthermore, it is expected that the mathematical understanding of the system can be lead to control the self-organization mechanism. In the study, we did several simulations with our proposed model for the Liesegang type precipitation, and we witnessed the relation between the final pattern and the external noise. Although, when it came to the contraction which goal is mathematical analysis, unfortunately, we could not obtain satisfactory result, however, we would like to conclude that there is a potential of future development based on the suggestion we got from the simulation.