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oai:recercat.cat:10230/439722025-12-20T17:00:23Zcom_2072_6col_2072_452952

On the behaviour of stochastic heat equations on bounded domains Foondun, Mohammud Nualart, Eulàlia Stochastic partial differential equations 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. Research supported in part by the European Union programme FP7-PEOPLE-2012-CIG under grant agreement 333938. 2020-03-20T08:49:04Z 2020-03-20T08:49:04Z 2015 info:eu-repo/semantics/article info:eu-repo/semantics/publishedVersion 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. 1980-0436 http://hdl.handle.net/10230/43972 eng ALEA Latin American Journal of Probability and Mathematical Statistics. 2015;12(2):551-71. info:eu-repo/grantAgreement/EC/FP7/333938 © ALEA. Published at: http://alea.impa.br/english/index_v12.htm info:eu-repo/semantics/openAccess application/pdf application/pdf ALEA