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.
引用
收藏
页码:6806 / 6855
页数:50
相关论文
共 50 条
  • [41] THE OPTIMIZATION OF TIME-FREQUENCY CONTROL - USING NON-AUTONOMOUS TIME-DELAY FEEDBACK SYSTEMS AS EXAMPLE
    Kuo, Chi-Wei
    Suh, C. Steve
    PROCEEDINGS OF THE ASME INTERNATIONAL MECHANICAL ENGINEERING CONGRESS AND EXPOSITION, 2016, VOL. 4B, 2017,
  • [42] ON THE LOW-FREQUENCY AND HIGH-FREQUENCY LIMIT OF QUANTUM SCATTERING BY TIME-DEPENDENT POTENTIALS
    MARTIN, PA
    DEBIANCHI, MS
    JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 1995, 28 (08): : 2403 - 2427
  • [43] PERIODIC SOLUTIONS OF A DISCRET TIME NON-AUTONOMOUS RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH CONTROL
    Zeng, Zhijun
    COMMUNICATIONS OF THE KOREAN MATHEMATICAL SOCIETY, 2007, 22 (03): : 465 - 474
  • [44] Periodic Motions of the Non-autonomous Oseen-Navier-Stokes Flows Past a Moving Obstacle with Data in Lp-Spaces
    Nguyen, Thieu Huy
    Tran, Thi Kim Oanh
    VIETNAM JOURNAL OF MATHEMATICS, 2024, 52 (01) : 219 - 233
  • [45] Human interaural time difference thresholds for sine tones: The high-frequency limit
    Brughera, Andrew
    Dunai, Larisa
    Hartmann, William M.
    JOURNAL OF THE ACOUSTICAL SOCIETY OF AMERICA, 2013, 133 (05): : 2839 - 2855
  • [46] Time periodic traveling waves in a three-component non-autonomous and reaction-diffusion epidemic model
    Wei, Jingdong
    Zhou, Jiangbo
    Zhen, Zaili
    Tian, Lixin
    INTERNATIONAL JOURNAL OF MATHEMATICS, 2021, 32 (01)
  • [47] Existence of Periodic Solutions to Non-autonomous Delay Cohen-Grossberg Neural Networks with Impulses on Time Scales
    Li, Zhouhong
    ADVANCES IN NEURAL NETWORKS - ISNN 2016, 2016, 9719 : 211 - 220
  • [48] Carrier-Domain Method for high-resolution computation of time-periodic long-wake flows
    Liu, Yang
    Takizawa, Kenji
    Tezduyar, Tayfun E.
    Kuraishi, Takashi
    Zhang, Yufei
    COMPUTATIONAL MECHANICS, 2023, 71 (01) : 169 - 190
  • [49] Carrier-Domain Method for high-resolution computation of time-periodic long-wake flows
    Yang Liu
    Kenji Takizawa
    Tayfun E. Tezduyar
    Takashi Kuraishi
    Yufei Zhang
    Computational Mechanics, 2023, 71 : 169 - 190
  • [50] Deformation of a two-dimensional viscoelastic drop at non-zero Reynolds number in time-periodic extensional flows
    Sarkar, K
    Schowalter, WR
    JOURNAL OF NON-NEWTONIAN FLUID MECHANICS, 2000, 95 (2-3) : 315 - 342