Convergence of invariant measures for singular stochastic diffusion equations
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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Volume (Year): 122 (2012)
Issue (Month): 4 ()
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- Barbu, Viorel & Da Prato, Giuseppe, 2010. "Invariant measures and the Kolmogorov equation for the stochastic fast diffusion equation," Stochastic Processes and their Applications, Elsevier, vol. 120(7), pages 1247-1266, July.
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