Gradient flows of time-dependent functionals in metric spaces and applications to PDEs

DOI10.1007/s00605-017-1037-yzbMath1390.35407arXiv1509.04161OpenAlexW2962997915MaRDI QIDQ681476

Lucas C. F. Ferreira, Julio C. Valencia-Guevara

Publication date: 12 February 2018

Published in: Monatshefte für Mathematik (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1509.04161

zbMATH Keywords

optimal transportgradient flowsmeasure solutionstime-dependent functionals

Mathematics Subject Classification ID

Variational inequalities (49J40) Variational problems in a geometric measure-theoretic setting (49Q20) Nonlinear differential equations in abstract spaces (34G20) Diffusion processes (60J60) Spaces of measures, convergence of measures (28A33) Initial value problems for second-order parabolic equations (35K15) Operator partial differential equations (= PDEs on finite-dimensional spaces for abstract space valued functions) (35R20) Partial differential equations of mathematical physics and other areas of application (35Qxx) Variational problems in infinite-dimensional spaces (58Exx)

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Gradient flow formulation and longtime behaviour of a constrained Fokker-Planck equation, Swarm gradient dynamics for global optimization: the mean-field limit case, Gradient flow for the Boltzmann entropy and Cheeger's energy on time-dependent metric measure spaces, Short retractions of CAT(1) spaces, A variational formulation of the BDF2 method for metric gradient flows, Well-posedness of evolution equations with time-dependent nonlinear mobility: a modified minimizing movement scheme

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