论文标题
随机shigesada-kawasaki-teramoto人口模型的全球martingale解决方案
Global martingale solutions for stochastic Shigesada-Kawasaki-Teramoto population models
论文作者
论文摘要
证明了全球非负MARTINGALE解决方案对具有乘法噪声的Shigesada-Kawasaki-teramoto类型的交叉扩散系统的存在。该模型描述了在没有升华边界条件的有限域中任意数量的人口物种的随机分离动力学。扩散矩阵通常既不是对称的，也不是阳性半芬矿，它不包括进化方程的标准方法。取而代之的是，存在证明是基于模型的熵结构，熵变量的新颖正则化，高阶估计和分数时间的规律性。正则化技术是通用的，并适用于在任何空间维度上具有自扩散的人口系统，并且在两个空间维度中无需自扩散。
The existence of global nonnegative martingale solutions to cross-diffusion systems of Shigesada-Kawasaki-Teramoto type with multiplicative noise is proven. The model describes the stochastic segregation dynamics of an arbitrary number of population species in a bounded domain with no-flux boundary conditions. The diffusion matrix is generally neither symmetric nor positive semidefinite, which excludes standard methods for evolution equations. Instead, the existence proof is based on the entropy structure of the model, a novel regularization of the entropy variable, higher-order moment estimates, and fractional time regularity. The regularization technique is generic and is applied to the population system with self-diffusion in any space dimension and without self-diffusion in two space dimensions.
