泊松白噪声驱动的一维随机波动方程
One-Dimensional Stochastic Wave Equations Driven by Poisson White Noise
摘要:
偏微分方程是一种确定性方程，虽然在多个领域具有广泛应用，但是不能很好的描述不确定的情况，因此探究随机噪声驱动的偏微分方程方程显得十分重要，所以本文主要利用了Picard迭代和Gronwall不等式证明了在一定条件下泊松白噪声驱动的一维随机波动方程的mild解的存在性和唯一性。
Abstract:
Partial differential equation is a kind of deterministic equations, although with wide applications in many fields, but not a good description of uncertain situation, thus to explore the partial differential equation of random noise drive equation is very important, so this paper mainly use the Picard iteration and Gronwall inequality is proved under certain conditions poisson white noise driven one-dimensional random wave equation of mild existence and uniqueness of solution.
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