标题： 带有超线性漂移的随机反应扩散方程在$\mathbb{R}$上的大型偏差原理，由时空白噪声驱动 显示英文标题

标题： Large deviation principle for stochastic reaction-diffusion equations with super-linear drift on $\mathbb{R}$ driven by space-time white noise

摘要： 在本文中，我们考虑实线上具有超线性漂移的随机反应扩散方程 $\mathbb{R}$，其由时空白噪声驱动。 通过在空间 $C([0,T], C_{tem}(\mathbb{R}))$上修改的弱收敛方法建立了弗里德林-文策尔大偏差原理。 由于无界区域、时空白噪声以及没有耗散的超线性漂移项，获得本文的主要结果具有挑战性。 为了克服这些困难，设计的特殊范数在 $C([0,T], C_{tem}(\mathbb{R}))$上，随机卷积的一个阶矩估计以及两个非线性格罗纳尔瓦类型不等式起到了重要作用。 显示英文摘要

摘要： In this paper, we consider stochastic reaction-diffusion equations with super-linear drift on the real line $\mathbb{R}$ driven by space-time white noise. A Freidlin-Wentzell large deviation principle is established by a modified weak convergence method on the space $C([0,T], C_{tem}(\mathbb{R}))$. Obtaining the main result in this paper is challenging due to the setting of unbounded domain, the space-time white noise, and the superlinear drift term without dissipation. To overcome these difficulties, the special designed norm on $C([0,T], C_{tem}(\mathbb{R}))$, one order moment estimates of the stochastic convolution and two nonlinear Gronwall-type inequalities play an important role.