On the behaviour of stochastic heat equations on bounded domains

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• dc.contributor.author Foondun, Mohammud
• dc.contributor.author Nualart, Eulàlia
• dc.date.accessioned 2020-03-20T08:49:04Z
• dc.date.available 2020-03-20T08:49:04Z
• dc.date.issued 2015
• dc.description.abstract Consider the following equation ∂tut(x) = 1 2 ∂xxut(x) + λσ(ut(x))W˙ (t, x) on an interval. Under Dirichlet boundary condition, we show that in the long run, the second moment of the solution grows exponentially fast if λ is large enough. But if λ is small, then the second moment eventually decays exponentially. If we replace the Dirichlet boundary condition by the Neumann one, then the second moment grows exponentially fast no matter what λ is. We also provide various extensions.
• dc.description.sponsorship Research supported in part by the European Union programme FP7-PEOPLE-2012-CIG under grant agreement 333938.
• dc.format.mimetype application/pdf
• dc.identifier.citation Foondun M, Nualart E. On the behaviour of stochastic heat equations on bounded domains. ALEA Lat Am J Probab Math Stat. 2015;12(2):551-71.
• dc.identifier.issn 1980-0436
• dc.identifier.uri http://hdl.handle.net/10230/43972
• dc.language.iso eng
• dc.publisher ALEA
• dc.relation.ispartof ALEA Latin American Journal of Probability and Mathematical Statistics. 2015;12(2):551-71.
• dc.relation.projectID info:eu-repo/grantAgreement/EC/FP7/333938
• dc.rights © ALEA. Published at: http://alea.impa.br/english/index_v12.htm
• dc.rights.accessRights info:eu-repo/semantics/openAccess
• dc.subject.keyword Stochastic partial differential equations
• dc.title On the behaviour of stochastic heat equations on bounded domains
• dc.type info:eu-repo/semantics/article
• dc.type.version info:eu-repo/semantics/publishedVersion