2016年4月
Some effects of the noise intensity upon non-linear stochastic heat equations on [0,1]
STOCHASTIC PROCESSES AND THEIR APPLICATIONS
- 巻
- 126
- 号
- 4
- 開始ページ
- 1184
- 終了ページ
- 1205
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1016/j.spa.2015.10.014
- 出版者・発行元
- ELSEVIER SCIENCE BV
Various effects of the noise intensity upon the solution u(t, x) of the stochastic heat equation with Dirichlet boundary conditions on [0, 1] are investigated. We show that for small noise intensity, the pth moment of sup(x is an element of[0,1]) vertical bar u(t, x)vertical bar is exponentially stable, however, for large one, it grows at least exponentially. We also prove that the noise excitation of the pth energy of u(t, x) is 4, as the noise intensity goes to infinity. We formulate a common method to investigate the lower bounds of the above two different behaviors for large noise intensity, which are hard parts in Foondun and Joseph (2014), Foondun and Nualart (2015) and Khoshnevisan and Kim (2015). (C) 2015 Elsevier B.V. All rights reserved.
- リンク情報
- ID情報
-
- DOI : 10.1016/j.spa.2015.10.014
- ISSN : 0304-4149
- eISSN : 1879-209X
- Web of Science ID : WOS:000371837800009