An introduction to the analysis of gradients systems
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3022
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WIAS Preprints
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Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik
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Abstract
The present notes provide an extended version of a small lecture course (of 36 hours) given at the Humboldt-Universität zu Berlin in the Winter Term 2022/23. The material starting in Section 5.4 was added afterwards. The aim of these notes to give an introductory overview on the analytical approaches for gradient-flow equations in Hilbert spaces, Banach spaces, and metric spaces and to show that on the first entry level these theories have a lot in common. The theories and their specific setups are illustrated by suitable examples and counterexamples.
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Gradient-flow equations, dissipation potential, kinetic relation, Fenchel equivalences, Fréchet subdifferentials, time-incremental minimization, abstract chain rule, energy-dissipation balance, energy-dissipation principle, minimizing movements, metric slope and metric speed, curves of maximal slope, De Giorgi lemma,, evolutionary Gamma-convergence
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CC BY 4.0 Unported