Abstract
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.
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Wolf-Jürgen Beyn and Janosch Rieger work supported by DFG in the framework of CRC 701, project B3. Etienne Emmrich work supported by DFG in the framework of CRC 910, project A8.
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Beyn, WJ., Emmrich, E. & Rieger, J. Semilinear parabolic differential inclusions with one-sided Lipschitz nonlinearities. J. Evol. Equ. 18, 1319–1339 (2018). https://doi.org/10.1007/s00028-018-0443-5
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DOI: https://doi.org/10.1007/s00028-018-0443-5
Keywords
- Analysis of partial differential inclusions
- Semilinear parabolic inclusion
- Relaxed one-sided Lipschitz condition
- Galerkin method
- Convergence of solution sets