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 a stochastic Shigesada-Kawasaki-Teramoto population model
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。该模型描述了种群具有任意数量的种群的隔离动力学。扩散矩阵通常既不是对称的，也不是阳性半限定，它不包括标准方法。取而代之的是，存在证明是基于模型的熵结构，该模型是由Wong-Zakai参数近似的，以及适当的更高矩估计和分数时间的规律性。在没有自扩散的情况下，通过仔细利用熵的生产条款来克服缺乏规律性。
The existence of global nonnegative martingale solutions to a cross-diffusion system of Shigesada-Kawasaki-Teramoto type with multiplicative noise is proven. The model describes the segregation dynamics of populations with an arbitrary number of species. The diffusion matrix is generally neither symmetric nor positive semidefinite, which excludes standard methods. Instead, the existence proof is based on the entropy structure of the model, approximated by a Wong-Zakai argument, and on suitable higher moment estimates and fractional time regularity. In the case without self-diffusion, the lack of regularity is overcome by carefully exploiting the entropy production terms.
