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This paper is dedicated to providing new tools and methods for studying the trend to equilibrium of gradient flows in metric spaces in the entropy and metric sense, to establish decay rates, finite time of extinction, and to characterize Lyapunov stable equilibrium points.
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by same author, Calculus and heat flow in metric measure spaces and applications to spaces with Ricci bounds from below , Invent. Math. 195
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by same author, Lecture notes on gradient flows and optimal transport , Optimal transportation, London Math. Soc. Lecture Note Ser., vol. 413, Cambridge Univ. Press, Cambridge, 2014, pp. 100–144
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P. M. N. Feehan, Global existence and convergence of solutions to gradient systems and applications to Yang-Mills gradient flow , ArXiv e-prints (2014)
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2018
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R. Chill and S. Mildner, The Kurdyka-łojasiewicz-Simon inequality and stabilisation in nonsmooth infinite-dimensional gradient systems , Proc. Amer. Math. Soc. 146
2018
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