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Stochastic Porous Media Equation on General Measure Spaces with Increasing Lipschitz Nonlinearties

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      Abstract

      We prove the existence and uniqueness of probabilistically strong solutions to stochastic porous media equations driven by time-dependent multiplicative noise on a general measure space \((E, \mathscr{B}(E), \mu)\), and the Laplacian replaced by a self-adjoint operator \(L\). In the case of Lipschitz nonlinearities \(\Psi\), we in particular generalize previous results for open \(E\subset \mathbb{R}^d\) and \(L\!\!=\)Laplacian to fractional Laplacians. We also generalize known results on general measure spaces, where we succeeded in dropping the transience assumption on \(L\), in extending the set of allowed initial data and in avoiding the restriction to superlinear behavior of \(\Psi\) at infinity for \(L^2(\mu)\)-initial data.

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      • Record: found
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      A harmonic calculus on the Sierpinski spaces

       Jun Kigami (1989)
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        Dirichlet forms on fractals and products of random matrices

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          • Record: found
          • Abstract: not found
          • Article: not found

          Stochastic generalized porous media and fast diffusion equations

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            Author and article information

            Journal
            2016-06-09
            1606.03001

            http://arxiv.org/licenses/nonexclusive-distrib/1.0/

            Custom metadata
            60H15, 76S05
            18pages
            math.PR

            Probability

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