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Stochastic Porous Media Equation on General Measure Spaces with Increasing Lipschitz Nonlinearties
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 , and the Laplacian
replaced by a self-adjoint operator . In the case of Lipschitz
nonlinearities , we in particular generalize previous results for open
and Laplacian to fractional Laplacians. We also
generalize known results on general measure spaces, where we succeeded in
dropping the transience assumption on , in extending the set of allowed
initial data and in avoiding the restriction to superlinear behavior of
at infinity for -initial data.Comment: 18page
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