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2016 | OriginalPaper | Chapter

3. Equations with Maximal Monotone Nonlinearities

Authors : Viorel Barbu, Giuseppe Da Prato, Michael Röckner

Published in: Stochastic Porous Media Equations

Publisher: Springer International Publishing

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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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previous chapter Equations with Lipschitz Nonlinearities
next chapter Variational Approach to Stochastic Porous Media Equations
Footnotes
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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Metadata
Title
Equations with Maximal Monotone Nonlinearities
Authors
Viorel Barbu
Giuseppe Da Prato
Michael Röckner
Copyright Year
2016
Book
Stochastic Porous Media Equations

Print ISBN: 978-3-319-41068-5

Electronic ISBN: 978-3-319-41069-2

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-319-41069-2_3