Abstract
AbstractIn 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.
Funder
Albert-Ludwigs-Universität Freiburg im Breisgau
Publisher
Springer Science and Business Media LLC
Subject
Mathematics (miscellaneous)
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