Convergence of invariant measures for singular stochastic diffusion equations |
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Authors: | Ioana Ciotir,Jonas M. Tö lle |
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Affiliation: | 1. Department of Mathematics, Faculty of Economics and Business Administration, “Al. I. Cuza” University, Bd. Carol no. 9–11, Ia?i, Romania;2. Institut für Mathematik, Technische Universität Berlin (MA 7-5), Straße des 17. Juni 136, 10623 Berlin, Germany |
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Abstract: | It is proved that the solutions to the singular stochastic p-Laplace equation, p∈(1,2) and the solutions to the stochastic fast diffusion equation with nonlinearity parameter r∈(0,1) on a bounded open domain Λ⊂Rd with Dirichlet boundary conditions are continuous in mean, uniformly in time, with respect to the parameters p and r respectively (in the Hilbert spaces L2(Λ), H−1(Λ) respectively). The highly singular limit case p=1 is treated with the help of stochastic evolution variational inequalities, where P-a.s. convergence, uniformly in time, is established. |
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Keywords: | 60H15 35K67 37L40 49J45 |
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