Reaction-diffusion systems: hysteresis and nonlocal interactions (A09*)

反应扩散系统：滞后和非局部相互作用 (A09*)

• 批准号: 265723286
• 金额: --
• 依托单位: Institut für Mathematik
• 依托单位国家: 德国
• 项目类别: Collaborative Research Centres
• 财政年份: 2015
• 资助国家: 德国
• 起止时间: 2014-12-31 至 2017-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/265723286?language=en
• 关键词: Reaction; diffusion; systems; hysteresis; nonlocal

The project deals with reaction-diffusion systems involving hysteresis, or, more generally, bistability. The models under consideration have applications to a large number of biological, chemical, physical, and economic processes. Besides the nontrivial issue of well-posedness, we are interested in the qualitative description of solutions. The analysis will be in terms of emerging spatio-temporal patterns that are influenced primarily by the interplay between diffusion and spatially distributed hysteresis. We will also develop theoretical concepts for the stability analysis and control of these patterns by temporally and spatially nonlocal feedback.

该项目处理涉及滞后的反应扩散系统，或者更一般地说，双稳定性。所考虑的模型可以应用于大量的生物、化学、物理和经济过程。除了适位性的重要问题外，我们对解的定性描述也很感兴趣。分析将从主要受扩散和空间分布迟滞之间相互作用影响的新出现的时空格局的角度进行。我们还将通过时间和空间非局部反馈发展稳定性分析和控制这些模式的理论概念。