論文

2016年4月

Some effects of the noise intensity upon non-linear stochastic heat equations on [0,1]

STOCHASTIC PROCESSES AND THEIR APPLICATIONS
  • Bin Xie

126
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
DOI
https://doi.org/10.1016/j.spa.2015.10.014
Web of Science
https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcAuth=JSTA_CEL&SrcApp=J_Gate_JST&DestLinkType=FullRecord&KeyUT=WOS:000371837800009&DestApp=WOS_CPL
ID情報
  • DOI : 10.1016/j.spa.2015.10.014
  • ISSN : 0304-4149
  • eISSN : 1879-209X
  • Web of Science ID : WOS:000371837800009

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