Control of travelling and rotating waves in spatially extended nonlinear systems (B06)

我们的目标是控制主动媒体中的自组织时空模式。特别是，我们引导非线性波和移动本地化点根据一个给定的协议内的二维和三维域的运动。为了达到我们的控制目标，我们应用基于多尺度扰动理论的方法进行位置和形状控制，并利用偏微分方程的最优控制，包括稀疏控制和逐点状态约束的强大方法。此外，我们调查的影响，空间限制波和现场动力学和研究反应扩散过程中的小隔间。

We aim at controlling self-organized spatio-temporal patterns in active media. In particular, we guide non-linear waves and moving localized spots according to a given protocol of movement within two- and three-dimensional domains. To reach our control goals we apply methods based on multiple scale perturbation theory for position and shape control and exploit the powerful methods of optimal control of partial differential equations including sparse control and pointwise state constraints. Additionally, we investigate the impact of spatial confinement on wave and spot dynamics and study reaction-diffusion processes in small compartments.