论文标题
网络上的随机反应扩散方程
Stochastic reaction-diffusion equations on networks
论文作者
论文摘要
我们考虑以有限图表示的有限网络上的随机反应扩散方程。在图中的每个边缘上，乘数圆柱性高斯噪声驱动的反应扩散方程是由动态的kirchhoff型定律补充的，该定律受到人物中的乘法标量高斯噪声的扰动。每个边缘上的反应项被认为是一个奇怪的多项式，不一定在每个边缘上具有相同的程度，可能是随机系数和负指数。我们利用Banach空间中随机进化方程的半群方法来获得图表上连续函数的样品路径的溶液的存在和独特性。为此，我们将现有结果推广到Banach空间中的抽象随机反应扩散方程。
We consider stochastic reaction-diffusion equations on a finite network represented by a finite graph. On each edge in the graph a multiplicative cylindrical Gaussian noise driven reaction-diffusion equation is given supplemented by a dynamic Kirchhoff-type law perturbed by multiplicative scalar Gaussian noise in the vertices. The reaction term on each edge is assumed to be an odd degree polynomial, not necessarily of the same degree on each edge, with possibly stochastic coefficients and negative leading term. We utilize the semigroup approach for stochastic evolution equations in Banach spaces to obtain existence and uniqueness of solutions with sample paths in the space of continuous functions on the graph. In order to do so we generalize existing results on abstract stochastic reaction-diffusion equations in Banach spaces.
