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Equations with Lipschitz Nonlinearities

  • Viorel Barbu
  • Giuseppe Da Prato
  • Michael Röckner
Chapter
Part of the Lecture Notes in Mathematics book series (LNM, volume 2163)

Abstract

We start here by studying the porous media equation problem (1.1) when \(\beta: \mathbb{R} \rightarrow \mathbb{R}\) is monotonically increasing and Lipschitz continuous. The main reason is that general maximal monotone graphs β can be approximated by their Yosida approximations β ε which are Lipschitz continuous and monotonically increasing. So, several estimates proved in this chapter will be exploited later for studying problems with more general β.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Viorel Barbu
    • 1
  • Giuseppe Da Prato
    • 2
  • Michael Röckner
    • 3
  1. 1.Department of MathematicsAl. I. Cuza University & Octav Mayer Institute of Mathematics of the Romanian AcademyIasiRomania
  2. 2.Classe di ScienzeScuola Normale Superiore di PisaPisaItaly
  3. 3.Department of MathematicsUniversity of BielefeldBielefeldGermany

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