Journal of Evolution Equations

, Volume 18, Issue 3, pp 1319–1339 | Cite as

Semilinear parabolic differential inclusions with one-sided Lipschitz nonlinearities

  • Wolf-Jürgen BeynEmail author
  • Etienne Emmrich
  • Janosch Rieger


We present an existence result for a partial differential inclusion with linear parabolic principal part and relaxed one-sided Lipschitz multivalued nonlinearity in the framework of Gelfand triples. Our study uses discretizations of the differential inclusion by a Galerkin scheme, which is compatible with a conforming finite element method, and we analyze convergence properties of the discrete solution sets.


Analysis of partial differential inclusions Semilinear parabolic inclusion Relaxed one-sided Lipschitz condition Galerkin method Convergence of solution sets 

Mathematics Subject Classification

Primary: 35R70 65M60 Secondary: 35K20 35K91 49J53 


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Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  • Wolf-Jürgen Beyn
    • 1
    Email author
  • Etienne Emmrich
    • 2
  • Janosch Rieger
    • 3
  1. 1.Department of MathematicsBielefeld UniversityBielefeldGermany
  2. 2.Institute of MathematicsTechnical University of BerlinBerlinGermany
  3. 3.School of Mathematical SciencesMonash UniversityMelbourneAustralia

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