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Existence of Curves of Maximal Slope and their Variational Approximation

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Gradient Flows

Part of the book series: Lectures in Mathematics ETH Zürich ((LM))

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Abstract

The main object of our investigation is the solution of the following Cauchy problem in the complete metric space (, d): Problem 2.0.1. Given a functional φ: → (−∞,+∞] and an initial datum u0D(φ), find a (p-)curve u of maximal slope in (0,+∞) for φ such that u(0+) = u0.

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© 2008 Birkhäuser Verlag AG

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(2008). Existence of Curves of Maximal Slope and their Variational Approximation. In: Gradient Flows. Lectures in Mathematics ETH Zürich. Birkhäuser Basel. https://doi.org/10.1007/978-3-7643-8722-8_4

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