Note on the existence theory for pseudo-monotone evolution problems

2019/05/31 by Kaltenbach, Alex, Růžička, Michael · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1905.13591

Abstract

In this note we develop a framework which allows to prove an existence result for non-linear 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 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.

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• Existence of global weak solutions to a parabolic p-Laplacian problem with convective term

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