论文标题
具有无界扩散的半线性SPDE的强溶液
Strong solutions of semilinear SPDEs with unbounded diffusion
论文作者
论文摘要
我们证明了使用分解方法对2平滑的Banach空间中随机卷积的经典最大不等式进行了修改。这允许通过轻度溶液方法来研究由圆柱布朗尼运动驱动的无界扩散算子的半线性随机部分微分方程。在有限的尺寸驾驶噪声的情况下，在系数上提供了足够的规律性，我们确定了强溶液的存在和独特性。
We prove a modification to the classical maximal inequality for stochastic convolutions in 2-smooth Banach spaces using the factorization method. This permits to study semilinear stochastic partial differential equations with unbounded diffusion operators driven by cylindrical Brownian motion via the mild solution approach. In the case of finite dimensional driving noise, provided sufficient regularity on the coefficients, we establish existence and uniqueness of strong solutions.
