Some non-existence results for a class of stochastic partial differential equations

Mohammud Foondun, Wei Liu, Erkan Nane

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)
18 Downloads (Pure)

Abstract

Considerthe following stochastic partial differential equation,

tut(x)=Lut(x)+σ(ut(x))F˙(t,x)t>0andxRd.

The operator L is thegenerator of a strictly stable process and F˙ is the random forcing term whichis assumed to be Gaussian. Under some additional conditions, most notably on σ and the initial condition, weshow non-existence of global random field solutions. Our results are new andcomplement earlier works.

Original languageEnglish
Pages (from-to)2575-2596
Number of pages22
JournalJournal of Differential Equations
Volume266
Issue number5
Early online date23 Aug 2018
DOIs
Publication statusPublished - 15 Feb 2019

Keywords

  • probability
  • partial differential equation
  • space–time white noise
  • space colored noise
  • fractional stochastic equation

Fingerprint Dive into the research topics of 'Some non-existence results for a class of stochastic partial differential equations'. Together they form a unique fingerprint.

Cite this