论文标题
随机步行空间上的Cahn-Hilliard方程
Cahn-Hilliard Equations on Random Walk Spaces
论文作者
论文摘要
在本文中，我们研究了随机步行空间框架中的非本地Cahn-Hilliard模型（CHE），其中包括特定情况，在本地加权连接的图形上，CHE由有限的Markov链或Cahn-Hilliard方程确定，由CAHN-HILLIARD方程式确定，由卷积可卷积可集成的集成核。我们考虑了该阶段和化学电位的不同过渡，以及包括障碍物（包括障碍物）的大量潜力。我们证明了Cahn-Hilliard方程的$ l^1 $中解决方案的存在和独特性。我们还表明，Cahn-Hilliard方程是Ginzburg-Landau自由能在适当的Hilbert空间上起作用的梯度流。我们最终研究了解决方案的渐近行为。
In this paper we study a nonlocal Cahn-Hilliard model (CHE) in the framework of random walk spaces, which includes as particular cases, the CHE on locally finite weighted connected graphs, the CHE determined by finite Markov chains or the Cahn-Hilliard Equations driven by convolution integrable kernels. We consider different transitions for the phase and the chemical potential, and a large class of potentials including obstacle ones. We prove existence and uniqueness of solutions in $L^1$ of the Cahn-Hilliard Equation. We also show that the Cahn-Hilliard equation is the gradient flow of the Ginzburg-Landau free energy functional on an appropriate Hilbert space. We finally study the asymptotic behaviour of the solutions.
