论文标题
全球Martingale解决方案，用于随机超级shigesada-kawasaki-teramoto型人口系统
Global martingale solutions to a stochastic superquadratic Shigesada-Kawasaki-Teramoto type population system
论文作者
论文摘要
对于具有超第二过渡速率的随机交叉扩散种群系统，我们表明存在全球的Martingale解决方案。我们依靠Galerkin近似方案来得出近似溶液的序列。我们将IT $ \ rm \ hat {o} $公式应用于得出统一的估计。根据估计，证明紧密度的属性后，更改空间的结果被用于确认限制是交叉扩散系统的martingale解决方案。我们注意到，在统一的估计过程中，我们必须引入辅助序列。近似序列的估计必须在辅助序列的估计上得出，这是这项工作的关键思想。
For a stochastic cross-diffusion population system with superquadratic transition rate, we show that a global martingale solution exists. We rely on the Galerkin approximation scheme to derive the sequence of approximated solutions. We apply the It$\rm\hat{o}$ formula to derive uniform estimates. After the tightness property be proved based on the estimation, a space changing result then be used to confirm the limit is a martingale solution of the cross-diffusion system. We notice that in the uniform estimation process, we have to introduce an auxiliary sequence. The estimation of the approximated sequence has to be derived on the estimation of the auxiliary sequence, which is the key idea of this work.
