论文标题
Martingale解决方案，用于随机趋化系统，具有多孔培养基扩散
Martingale Solution to a Stochastic Chemotaxis System with Porous Medium Diffusion
论文作者
论文摘要
在本文中，我们研究了经典的凯勒 - Segel系统，这是一个二维领域，该结构域受到一对Wiener过程的干扰，其中领先的扩散项被多孔介质术语代替。由于随机性是固有的，因此在Stratonovich意义上对随机积分的解释是自然的。我们构建一个解决方案（积分）操作员，并在适当选择的Banach空间中建立其连续性和紧凑性。通过这种方式，我们制定了Schauder -Tychonoff类型固定点定理的随机版本，该定理特定于我们的问题以获得解决方案。实物，我们实现了Martingale解决方案的存在。
In this paper, we study the classical Keller - Segel system on a two-dimensional domain perturbed by a pair of Wiener processes, where the leading diffusion term is replaced by a porous media term. Since the randomness is intrinsic, the interpretation of the stochastic integral in the Stratonovich sense is natural. We construct a solution (integral) operator and establish its continuity and compactness properties in an appropriately chosen Banach space. In this manner, we formulate a stochastic version of the Schauder - Tychonoff Type Fixed Point Theorem which is specific to our problem to obtain a solution. In-kind, we achieve the existence of a martingale solution.
