scholarly journals Numerical analysis of a parabolic variational inequality system modeling biofilm growth at the porescale

2020 ◽  
Vol 36 (5) ◽  
pp. 941-971
Author(s):  
Azhar Alhammali ◽  
Malgorzata Peszynska
Keyword(s):  
Variational Inequality ◽  
Numerical Analysis ◽  
System Modeling ◽  
Biofilm Growth ◽  
Parabolic Variational Inequality ◽  
Inequality System

scholarly journals Topological degree and application to a parabolic variational inequality problem

2001 ◽  
Vol 25 (4) ◽  
pp. 273-287 ◽  
Author(s):  
A. Addou ◽  
B. Mermri
Keyword(s):  
Variational Inequality ◽  
Topological Degree ◽  
Variational Inequality Problem ◽  
Maximal Monotone ◽  
Maximal Monotone Operators ◽  
Monotone Operators ◽  
Parabolic Variational Inequality ◽  
Inequality Problem ◽  
Monotone Map ◽  
New Formulation

We are interested in constructing a topological degree for operators of the formF=L+A+S, whereLis a linear densely defined maximal monotone map,Ais a bounded maximal monotone operators, andSis a bounded demicontinuous map of class(S+)with respect to the domain ofL. By means of this topological degree we prove an existence result that will be applied to give a new formulation of a parabolic variational inequality problem.

Higher-order parabolic variational inequality in unbounded domains

2008 ◽  
Vol 60 (7) ◽  
pp. 1114-1135
Author(s):  
I. M. Medvid’
Keyword(s):  
Variational Inequality ◽  
Unbounded Domains ◽  
Higher Order ◽  
Parabolic Variational Inequality

A NUMERICAL ANALYSIS OF A REACTION–DIFFUSION SYSTEM MODELING THE DYNAMICS OF GROWTH TUMORS

2010 ◽  
Vol 20 (05) ◽  
pp. 731-756 ◽  
Author(s):  
VERÓNICA ANAYA ◽  
MOSTAFA BENDAHMANE ◽  
MAURICIO SEPÚLVEDA
Keyword(s):  
Weak Solution ◽  
Numerical Analysis ◽  
Numerical Scheme ◽  
System Modeling ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Existence Of Weak Solutions ◽  
Early Tumor ◽  
Volume Method

We consider a reaction–diffusion system of 2 × 2 equations modeling the spread of early tumor cells. The existence of weak solutions is ensured by a classical argument of Faedo–Galerkin method. Then, we present a numerical scheme for this model based on a finite volume method. We establish the existence of discrete solutions to this scheme, and we show that it converges to a weak solution. Finally, some numerical simulations are reported with pattern formation examples.

An OptimalL∞–error Estimate for an Approximation of a Parabolic Variational Inequality

2015 ◽  
Vol 37 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Mohamed Amine Bencheikh Le Hocine ◽  
Salah Boulaaras ◽  
Mohamed Haiour
Keyword(s):  
Variational Inequality ◽  
Error Estimate ◽  
Parabolic Variational Inequality
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