Note on the existence theory for pseudo-monotone evolution problems

In this note, we develop a framework which allows to prove an existence result for nonlinear evolution problems involving time-dependent, pseudo-monotone operators. This abstract existence result is applicable to a large class of concrete problems where the standard theorem on evolutionary pseudo-mo...

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Bibliographic Details
Published in:Journal of evolution equations 2021-03, Vol.21 (1), p.247-276
Main Authors: Kaltenbach, A., Růžička, M.
Format: Article
Language:English
Subjects:
Analysis
Coercivity
Evolution
Mathematics
Mathematics and Statistics
Operators
Theorems
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Summary:In this note, we develop a framework which allows to prove an existence result for nonlinear evolution problems involving time-dependent, pseudo-monotone operators. This abstract existence result is applicable to a large class of concrete problems where the standard theorem on evolutionary pseudo-monotone operators (cf. Theorem  1.3 ) is not applicable. To this end we introduce the notion of Bochner pseudo-monotonicity, and Bochner coercivity, which are appropriate extensions of the concepts of pseudo-monotonicity and coercivity to the evolutionary setting. Moreover, we give sufficient conditions for these new notions, which are easily and widely applicable.
ISSN:1424-3199
1424-3202
DOI:10.1007/s00028-020-00577-y