Existence and uniqueness of nonnegative solutions to the stochastic porous media equation

By Viorel Barbu, Giuseppe Da Prato, Michael Röckner. 2007

93 citations recorded by the source corpus.

It is proved that the stochastic porous media equation in a bounded domain of R 3 , with multiplicative noise, with a monotone nonlin- earity of polynomial growth has a unique nonnegative solution in H 1 (in particular is nonnegative measure-valued), provided the initial data is in H 1 and nonnegative.

Subfields: Computational Theory and Mathematics, Finance, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7dc07ac9275948bbfde02b4f45a85f435ab50b1b

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In Computational Theory and Mathematics

In Finance

In Mathematical Physics

Citations in the corpus

Random attractors for a class of stochastic partial differential equations driven by general additive noise (2010, background): “As a typical example of an SPDE in this framework stochastic porous media equations have been intensively investigated in [4, 5, 6, 7, 19, 27, 34, 36, 45].”
Stochastic non-isotropic degenerate parabolic–hyperbolic equations (2016, background): “ˆ T 0 ω̄ne −ω̄nr(|n|2r)− θ2 dr ˆ T 0 E‖χ̂(n, ·, r)‖2dr, and, in view of the fact that, for θ ∈ [0, 1],”
SPDE in Hilbert space with locally monotone coefficients (2010, background): “As one typical example of SPDE in this framework, the stochastic porous media equation has been extensively studied in [1, 2, 3, 4, 9, 31].”
Stochastic Variational Inequalities and Applications to the Total Variation Flow Perturbed by Linear Multiplicative Noise (2012, background): “2 in [7] or can be done similarly as in the proof of Theorem 7.”