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Equations with Maximal Monotone Nonlinearities

Part of the Lecture Notes in Mathematics book series (LNM,volume 2163)

Abstract

We shall study here Eq. (1.1) for general (multivalued) maximal monotone graphs \(\beta: \mathbb{R} \rightarrow 2^{\mathbb{R}}\) with polynomial growth. The principal motivation for the study of these equations comes from nonlinear diffusion models presented in Sect. 1.1

Keywords

  • Maximal Monotone
  • Stochastic Porous Media Equations
  • Linear Multiplicative Noise
  • Unique Distributional Solution
  • Rescaling Approach

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 1.

    c1 is the constant from the Burkholder–Davis–Gundy inequality (1.23).

  2. 2.

    Recall that \(\widetilde{\beta _{\epsilon }}(r) =\beta _{\epsilon }(r) +\epsilon r\) and \(\widetilde{\beta _{\eta }}(r) =\beta _{\eta }(r) +\eta r\), \(r \in \mathbb{R}\).

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Barbu, V., Da Prato, G., Röckner, M. (2016). Equations with Maximal Monotone Nonlinearities. In: Stochastic Porous Media Equations. Lecture Notes in Mathematics, vol 2163. Springer, Cham. https://doi.org/10.1007/978-3-319-41069-2_3

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