Foondun, MohammudNualart, Eulàlia2020-03-202020-03-202015Foondun M, Nualart E. On the behaviour of stochastic heat equations on bounded domains. ALEA Lat Am J Probab Math Stat. 2015;12(2):551-71.1980-0436http://hdl.handle.net/10230/43972Consider 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.application/pdfeng© ALEA. Published at: http://alea.impa.br/english/index_v12.htminfo:eu-repo/semantics/articleStochastic partial differential equationsinfo:eu-repo/semantics/openAccess