论文标题
通过梯度流量方法构建具有奇异能量的两相流量
Construction of a two-phase flow with singular energy by gradient flow methods
论文作者
论文摘要
我们证明了两个扩散方程的系统的弱解，这些扩散方程与点数的体积约束结合在一起。时间演变由自由能函数的梯度动力学给出。我们的主要示例是聚合物混合的模型，相应的能量是弗洛里，霍金斯和degennes之一。由于方程式中的非局部性，此处考虑的动力学与正式相关的Cahn-Hilliard方程中的动力学不同。 Our angle of attack is from the theory of optimal mass transport, that is, we consider the evolution equations for the two components as two gradient flows in the Wasserstein distance with one joint energy functional that has the volume constraint built in. The main difference to our previous work arXiv:1712.06446 is the nonlinearity of the energy density in the gradient part, which becomes singular at the interface between pure and mixed phases.
We prove the existence of weak solutions to a system of two diffusion equations that are coupled by a pointwise volume constraint. The time evolution is given by gradient dynamics for a free energy functional. Our primary example is a model for the demixing of polymers, the corresponding energy is the one of Flory, Huggins and deGennes. Due to the non-locality in the equations, the dynamics considered here is qualitatively different from the one found in the formally related Cahn-Hilliard equations. Our angle of attack is from the theory of optimal mass transport, that is, we consider the evolution equations for the two components as two gradient flows in the Wasserstein distance with one joint energy functional that has the volume constraint built in. The main difference to our previous work arXiv:1712.06446 is the nonlinearity of the energy density in the gradient part, which becomes singular at the interface between pure and mixed phases.
