High-frequency limit of non-autonomous gradient flows of functionals with time-periodic forcing

被引:2
|
作者
Plazotta, Simon [1 ]
Zinsl, Jonathan [1 ]
机构
[1] Tech Univ Munich, Zentrum Math, D-85747 Garching, Germany
关键词
Gradient flow; Wasserstein metric; Minimizing movements; Non-autonomous problem; Rapid oscillations; EVOLUTION-EQUATIONS; GRANULAR MEDIA; SYSTEM; DIFFUSION;
D O I
10.1016/j.jde.2016.09.003
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
We study the high-frequency limit of non-autonomous gradient flows in metric spaces of energy functionals comprising an explicitly time-dependent perturbation term which might oscillate in a rapid way. On grounds of the existence results by Ferreira and Guevara (2015) on non-autonomous gradient flows (which we also extend to a broader range of energy functionals), we prove that the associated solution curves converge to a solution of the time-averaged evolution equation in the limit of infinite frequency. Under additional assumptions on the energy, we obtain an explicit rate of convergence. Furthermore, we specifically investigate nonlinear drift-diffusion equations with time-dependent drift which formally are gradient flows with respect to the L-2-Wasserstein distance. We prove that a family of weak solutions obtained as a limit of the Minimizing Movements scheme exhibits the above-mentioned behavior in the high-frequency limit. (C) 2016 Elsevier Inc. All rights reserved.
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页码:6806 / 6855
页数:50
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