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
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Notes
- 1.
c1 is the constant from the Burkholder–Davis–Gundy inequality (1.23).
- 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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