Γ-CONVERGENCE AND RELAXATIONS FOR GRADIENT FLOWS IN METRIC SPACES: A MINIMIZING MOVEMENT APPROACH

被引：5

作者：

Fleissner, Florentine ^{[1
]}

机构：

[1] Tech Univ Munich, Zentrum Math, Boltzmannstr 3, D-85748 Garching, Germany

来源：

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS | 2019年 / 25卷

关键词：

Gradient flows; minimizing movements; Gamma-convergence; relaxation; curves of maximal slope; HILBERT;

D O I：

10.1051/cocv/2017035

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

We present new abstract results on the interrelation between the minimizing movement scheme for gradient flows along a sequence of Gamma-converging functionals and the gradient flow motion for the corresponding limit functional, in a general metric space. We are able to allow a relaxed form of minimization in each step of the scheme, and so we present new relaxation results too.

引用

页数：29

共 40 条

[21] CONVERGENCE OF A PARTICLE METHOD FOR DIFFUSIVE GRADIENT FLOWS IN ONE DIMENSION [J].

Carrillo, J. A. ;

Patacchini, F. S. ;

Sternberg, P. ;

Wolansky, G. .

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2016, 48 (06) :3708-3741

[22] A novel relaxed scalar auxiliary variable approach for gradient flows [J].

Liu, Zhengguang ;

He, Qing .

APPLIED MATHEMATICS LETTERS, 2023, 141

[23] A VARIATIONAL FORMULATION OF THE BDF2 METHOD FOR METRIC GRADIENT FLOWS [J].

Matthes, Daniel ;

Plazotta, Simon .

ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE, 2019, 53 (01) :145-172

[24] Metric gradient flows with state dependent functionals: The Nash-MFG equilibrium flows and their numerical schemes [J].

Turinici, Gabriel .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2017, 165 :163-181

[25] NONLINEAR DIFFUSION EQUATIONS WITH VARIABLE COEFFICIENTS AS GRADIENT FLOWS IN WASSERSTEIN SPACES [J].

Lisini, Stefano .

ESAIM-CONTROL OPTIMISATION AND CALCULUS OF VARIATIONS, 2009, 15 (03) :712-740

[26] CONVERGENCE AND ERROR ANALYSIS FOR THE SCALAR AUXILIARY VARIABLE (SAV) SCHEMES TO GRADIENT FLOWS [J].

Shen, Jie ;

Xu, Jie .

SIAM JOURNAL ON NUMERICAL ANALYSIS, 2018, 56 (05) :2895-2912

[27] The scalar auxiliary variable (SAV) approach for gradient flows [J].

Shen, Jie ;

Xu, Jie ;

Yang, Jiang .

JOURNAL OF COMPUTATIONAL PHYSICS, 2018, 353 :407-416

[28] Strong convergence for gradient projection method and relatively nonexpansive mappings in Banach spaces [J].

Nakajo, Kazuhide .

APPLIED MATHEMATICS AND COMPUTATION, 2015, 271 :251-258

[29] Variational approach to coarse-graining of generalized gradient flows [J].

Manh Hong Duong ;

Lamacz, Agnes ;

Peletier, Mark A. ;

Sharma, Upanshu .

CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2017, 56 (04)

[30] ENERGY STABILITY AND CONVERGENCE OF SAV BLOCK-CENTERED FINITE DIFFERENCE METHOD FOR GRADIENT FLOWS [J].

Li, Xiaoli ;

Shen, Jie ;

Rui, Hongxing .

MATHEMATICS OF COMPUTATION, 2019, 88 (319) :2047-2068

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