A numerical approach to the proof of existence of solutions for some generalized obstacle problems

2010 ◽  
Vol 216 (11) ◽  
pp. 3365-3369 ◽  
Author(s):  
Cheon Seoung Ryoo
Keyword(s):  
Existence Of Solutions ◽  
Numerical Approach ◽  
Obstacle Problems

scholarly journals Existence of Solutions for Implicit Obstacle Problems of Fractional Laplacian Type Involving Set-Valued Operators

2020 ◽  
Vol 187 (2) ◽  
pp. 391-407
Author(s):  
Dumitru Motreanu ◽  
Van Thien Nguyen ◽  
Shengda Zeng
Keyword(s):  
Fixed Point ◽  
Existence Theorem ◽  
Nonsmooth Analysis ◽  
Obstacle Problem ◽  
Fractional Laplacian ◽  
Existence Of Solutions ◽  
Obstacle Problems ◽  
Generalized Gradient ◽  
Fixed Point Principle ◽  
Set Valued Mappings

Abstract The paper is devoted to a new kind of implicit obstacle problem given by a fractional Laplacian-type operator and a set-valued term, which is described by a generalized gradient. An existence theorem for the considered implicit obstacle problem is established, using a surjectivity theorem for set-valued mappings, Kluge’s fixed point principle and nonsmooth analysis.

Existence of solutions for a class of obstacle problems with $$L^1$$ L 1 -data and without sign condition

2015 ◽  
Vol 27 (5-6) ◽  
pp. 795-813 ◽  
Author(s):  
Elhoussine Azroul ◽  
Mohamed Badr Benboubker ◽  
Hassane Hjiaj ◽  
Chihab Yazough
Keyword(s):  
Existence Of Solutions ◽  
Obstacle Problems ◽  
Sign Condition

A New Numerical Approach to Obstacle Problems

1995 ◽  
pp. 259-262
Author(s):  
Alain Cimetière ◽  
Thierry Texier
Keyword(s):  
Numerical Approach ◽  
Obstacle Problems

A numerical approach for odd-order obstacle problems

1994 ◽  
Vol 54 (1-2) ◽  
pp. 109-116 ◽  
Author(s):  
Muhammed Aslam Noor ◽  
Ahamed Kamel Khalifa
Keyword(s):  
Numerical Approach ◽  
Obstacle Problems ◽  
Odd Order

scholarly journals Finite State Graphon Games with Applications to Epidemics

2022 ◽  
Author(s):  
Alexander Aurell ◽  
René Carmona ◽  
Gökçe Dayanıklı ◽  
Mathieu Laurière
Keyword(s):  
Nash Equilibria ◽  
Existence Of Solutions ◽  
Numerical Approach ◽  
Mathematical Framework ◽  
Machine Learning Methods ◽  
Strength Of Interaction ◽  
Finite State ◽  
Heterogeneous Interactions ◽  
Fully Coupled ◽  
Finite State Space

AbstractWe consider a game for a continuum of non-identical players evolving on a finite state space. Their heterogeneous interactions are represented with a graphon, which can be viewed as the limit of a dense random graph. A player’s transition rates between the states depend on their control and the strength of interaction with the other players. We develop a rigorous mathematical framework for the game and analyze Nash equilibria. We provide a sufficient condition for a Nash equilibrium and prove existence of solutions to a continuum of fully coupled forward-backward ordinary differential equations characterizing Nash equilibria. Moreover, we propose a numerical approach based on machine learning methods and we present experimental results on different applications to compartmental models in epidemiology.

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