论文标题
具有奇异电位的随机抛物线方程
Stochastic parabolic equations with singular potentials
论文作者
论文摘要
在这项工作中，我们考虑了一类随机抛物线方程，其空间取决于潜在的，随机驱动力和随机初始条件。对于这些方程式的分析，我们将白噪声分析和非常弱的解决方案的概念结合了混乱的扩展方法。对于给定的随机抛物线方程，我们介绍了随机解决方案的概念，证明了对相应的随机初始值问题的非常弱解决方案的存在和唯一性，并在给定的奇异潜力上表现出正则化的独立性。另外，显示了随机弱溶液的随机非常弱溶液的一致性。
In this work we consider a class of stochastic parabolic equations with singular space depending potential, random driving force and random initial condition. For the analysis of these equations we combine the chaos expansion method from the white noise analysis and the concept of very weak solutions. For given stochastic parabolic equation we introduce the notion of a stochastic very weak solution, prove the existence and uniqueness of the very weak solution to corresponding stochastic initial value problem and show its independence of a regularization on given singular potential. In addition, the consistency of a stochastic very weak solution with a stochastic weak solution is shown.
