论文标题
在具有乘法噪声的网络上的随机allen-cahn方程上
On the stochastic Allen-Cahn equation on networks with multiplicative noise
论文作者
论文摘要
我们考虑了由有限图表示的有限网络上的随机allen-cahn方程系统。在图中的每个边缘上，都给出了乘型高斯噪声驱动的随机艾伦 - 卡纳方程，可能会在顶点中补充有连续性条件和基希霍夫型定律。使用BANACH空间中随机演化方程的半群方法，我们在图表上连续函数的空间中获得了溶液的存在和唯一性。我们还证明了解决方案的更精确的时空规律性。
We consider a system of stochastic Allen-Cahn equations on a finite network represented by a finite graph. On each edge in the graph a multiplicative Gaussian noise driven stochastic Allen-Cahn equation is given with possibly different potential barrier heights supplemented by a continuity condition and a Kirchhoff-type law in the vertices. Using the semigroup approach for stochastic evolution equations in Banach spaces we obtain existence and uniqueness of solutions with sample paths in the space of continuous functions on the graph. We also prove more precise space-time regularity of the solution.
