Large Deviation Principle for Stochastic Reaction–Diffusion Equations with Superlinear Drift on R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}$$\end{document} Driven by Space–Time White Noise

被引:0
作者
Yue Li [1 ]
Shijie Shang [1 ]
Jianliang Zhai [1 ]
机构
[1] University of Science and Technology of China,School of Mathematical Sciences
关键词
Stochastic reaction–diffusion equation; Large deviation principle; Unbounded domain; Space–time white noise; Weak convergence method; Superlinear drift term; Primary 60H15; Secondary 60F10; 35R60;
D O I
10.1007/s10959-024-01345-1
中图分类号
学科分类号
摘要
In this paper, we consider stochastic reaction–diffusion equations with superlinear drift on the real line R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathbb {R}$$\end{document} 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],Ctem(R))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C([0,T], C_\textrm{tem}(\mathbb {R}))$$\end{document}, where Ctem(R):={f∈C(R):supx∈R|f(x)|e-λ|x|<∞for anyλ>0}\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C_\textrm{tem}(\mathbb {R}):=\{f\in C(\mathbb {R}): \sup _{x\in \mathbb {R}} \left( |f(x)|e^{-\lambda |x|}\right) <\infty \text { for any } \lambda >0\}$$\end{document}. 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 specially designed family of norms on the Fréchet space C([0,T],Ctem(R))\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$C([0,T], C_\textrm{tem}(\mathbb {R}))$$\end{document}, one-order moment estimates of the stochastic convolution, and two nonlinear Gronwall-type inequalities play an important role.
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页码:3496 / 3539
页数:43
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