论文标题
与随机强迫的隔离交叉扩散系统的全球martingale解决方案
Global martingale solutions to a segregation cross-diffusion system with stochastic forcing
论文作者
论文摘要
显示了在具有无升华边界条件的有界域中具有乘法维纳噪声的交叉扩散系统的全局mar虫解决方案。该模型描述了由于隔离交叉扩散效应而导致不同物种的种群密度的动力学。扩散矩阵通常既不对称也不是阳性半芬矿。通过利用RAO熵结构来克服这一困难。存在证明使用随机的Galerkin方法，从RAO熵不等式中估计的均匀估计以及Skorokhod-Jakubowski定理。此外，通过使用相对RAO熵，证明了指数平衡的结果对于噪声的足够小的Lipschitz常数证明了指数平衡。数值测试说明了两个种群物种的一个空间维度中解决方案的行为。
The existence of a global martingale solution to a cross-diffusion system with multiplicative Wiener noise in a bounded domain with no-flux boundary conditions is shown. The model describes the dynamics of population densities of different species due to segregation cross-diffusion effects. The diffusion matrix is generally neither symmetric nor positive semidefinite. This difficulty is overcome by exploiting the Rao entropy structure. The existence proof uses a stochastic Galerkin method, uniform estimates from the Rao entropy inequality, and the Skorokhod--Jakubowski theorem. Furthermore, an exponential equilibration result is proved for sufficiently small Lipschitz constants of the noise by using the relative Rao entropy. Numerical tests illustrate the behavior of solutions in one space dimension for two and three population species.
