scholarly journals The Systems of Nonlinear Gradient Flows on Metric Spaces and Its Gamma-Convergence

2012 ◽  
Vol 2012 ◽  
pp. 1-18
Author(s):  
Mao-Sheng Chang ◽  
Bo-Cheng Lu
Keyword(s):  
Nonlinear System ◽  
Metric Spaces ◽  
Gradient Flow ◽  
Gamma Convergence ◽  
Gradient Flows ◽  
Energy Functionals ◽  
Several Variables ◽  
Flow Systems

We first establish the explicit structure of nonlinear gradient flow systems on metric spaces and then develop Gamma-convergence of the systems of nonlinear gradient flows, which is a scheme meant to ensure that if a family of energy functionals of several variables depending on a parameter Gamma-converges, then the solutions to the associated systems of gradient flows converge as well. This scheme is a nonlinear system edition of the notion initiated by Sylvia Serfaty in 2011.

Γ-convergence and relaxations for gradient flows in metric spaces: a minimizing movement approach

2019 ◽  
Vol 25 ◽  
pp. 28
Author(s):  
Florentine Fleißner
Keyword(s):  
Metric Space ◽  
Metric Spaces ◽  
Gradient Flow ◽  
Gradient Flows ◽  
Flow Motion ◽  
Limit Functional ◽  
Γ Convergence

We present new abstract results on the interrelation between the minimizing movement scheme for gradient flows along a sequence of Γ-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.

scholarly journals MINIMIZERS AND GAMMA-CONVERGENCE OF ENERGY FUNCTIONALS DERIVED FROM $p$-LAPLACIAN EQUATION

2009 ◽  
Vol 13 (6B) ◽  
pp. 2021-2036 ◽  
Author(s):  
Mao-Sheng Chang ◽  
Shu-Cheng Lee ◽  
Chien-Chang Yen
Keyword(s):  
Gamma Convergence ◽  
Energy Functionals ◽  
Laplacian Equation

scholarly journals On Ćirić-Prešić Operators in Metric Spaces

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Narongsuk Boonsri ◽  
Satit Saejung ◽  
Kittipong Sitthikul
Keyword(s):  
Fixed Point ◽  
Recent Result ◽  
Integral Equations ◽  
Metric Spaces ◽  
Fixed Point Problem ◽  
Point Problem ◽  
Classical Approach ◽  
Single Variable ◽  
Several Variables ◽  
Convergence Problems

We show that the Prešić type operators of several variables can be regarded as an operator of a single variable and the fixed point problem of Prešić type can be regarded as a classical fixed point problem. We extend the recent result of Ćirić and Prešić by using the classical approach of Prešić. The key of the proof is based on the mappings introduced by Kada, Suzuki, and Takahashi. We also discuss the convergence problems of recursive real sequences and the Volterra integral equations as an application of our result.

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