Semilinear parabolic differential inclusions with one-sided Lipschitz nonlinearities

Wolf Jürgen Beyn; Etienne Emmrich; Janosch Rieger

doi:10.1007/s00028-018-0443-5

Semilinear parabolic differential inclusions with one-sided Lipschitz nonlinearities

Wolf Jürgen Beyn, Etienne Emmrich, Janosch Rieger

School of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

4 Citations (Scopus)

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.

Original language	English
Pages (from-to)	1319-1339
Number of pages	21
Journal	Journal of Evolution Equations
Volume	18
Issue number	3
DOIs	https://doi.org/10.1007/s00028-018-0443-5
Publication status	Published - 2018

Keywords

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

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10.1007/s00028-018-0443-5

Cite this

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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.",

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

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AB - 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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KW - Convergence of solution sets

KW - Galerkin method

KW - Relaxed one-sided Lipschitz condition

KW - Semilinear parabolic inclusion

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Semilinear parabolic differential inclusions with one-sided Lipschitz nonlinearities

Abstract

Keywords

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