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• W2255369098 abstract "We develop a gradient-flow theory for time-dependent functionals defined in abstract metric spaces. Global well-posedness and asymptotic behavior of solutions are provided. Conditions on functionals and metric spaces allow to consider the Wasserstein space $mathscr{P}_{2}(mathbb{R}^{d})$ and apply the results for a large class of PDEs with time- dependent coefficients like confinement and interaction potentials and diffusion. Our results can be seen as an extension of those in Ambrosio-Gigli-Savar'e (2005)[2] to the case of time-dependent functionals. For that matter, we need to consider some residual terms, time-versions of concepts like $lambda$-convexity, time-differentiability of minimizers for Moreau-Yosida approximations, and a priori estimates with explicit time-dependence for De Giorgi interpolation. Here, functionals can be unbounded from below and satisfy a type of $lambda$-convexity that changes as the time evolves." @default.
• W2255369098 created "2016-06-24" @default.
• W2255369098 creator A5005215596 @default.
• W2255369098 creator A5047592688 @default.
• W2255369098 date "2015-09-14" @default.
• W2255369098 modified "2023-09-27" @default.
• W2255369098 title "Gradient flows of time-dependent functionals in metric spaces and applications for PDEs" @default.
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