论文标题
线性反应扩散系统具有快速可逆反应的EDP连接
EDP-convergence for a linear reaction-diffusion system with fast reversible reaction
论文作者
论文摘要
我们对线性反应扩散系统进行快速反应极限，该系统由两个通过线性反应结合的两个扩散方程组成。我们将线性反应扩散系统理解为具有几何结构的概率度量空间中的自由能的梯度流，其中包含用于扩散部分的Wasserstein度量，并为反应部分提供了COSH型功能。快速反应极限是在梯度结构水平上通过倾斜来证明EDP连接的。极限梯度系统在线性慢动作上诱导具有Lagrange乘数的扩散系统。此外，极限梯度系统可以通过粗粒梯度系统等效地描述，该系统可诱导粗粒慢速变量具有混合扩散常数的扩散方程。
We perform a fast-reaction limit for a linear reaction-diffusion system consisting of two diffusion equations coupled by a linear reaction. We understand the linear reaction-diffusion system as a gradient flow of the free energy in the space of probability measure equipped with a geometric structure, which contains the Wasserstein metric for the diffusion part and cosh-type functions for the reaction part. The fast-reaction limit is done on the level of the gradient structure by proving EDP-convergence with tilting. The limit gradient system induces a diffusion system with Lagrange multipliers on the linear slow-manifold. Moreover, the limit gradient system can be equivalently described by a coarse-grained gradient system, which induces a diffusion equation with a mixed diffusion constant for the coarse-grained slow variable.
