scholarly journals Numerical Analysis for a System Coupling Curve Evolution to Reaction Diffusion on the Curve

2017 ◽  
Vol 55 (2) ◽  
pp. 1080-1100 ◽  
Author(s):  
John W. Barrett ◽  
Klaus Deckelnick ◽  
Vanessa Styles
Keyword(s):  
Numerical Analysis ◽  
Reaction Diffusion ◽  
Curve Evolution ◽  
System Coupling

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.

scholarly journals Generalized principal eigenvalues for heterogeneous road–field systems

2019 ◽  
Vol 22 (01) ◽  
pp. 1950013 ◽  
Author(s):  
Henri Berestycki ◽  
Romain Ducasse ◽  
Luca Rossi
Keyword(s):  
Nonlinear Evolution Equation ◽  
Ecological Niche ◽  
Nonlinear Evolution ◽  
Principal Eigenvalue ◽  
Reaction Diffusion ◽  
Fast Diffusion ◽  
Reaction Diffusion Model ◽  
Math Biol ◽  
Field Systems ◽  
System Coupling

This paper develops the notion and properties of the generalized principal eigenvalue for an elliptic system coupling an equation in a plane with one on a line in this plane, together with boundary conditions that express exchanges taking place between the plane and the line. This study is motivated by the reaction–diffusion model introduced by Berestycki, Roquejoffre and Rossi [The influence of a line with fast diffusion on Fisher–KPP propagation, J. Math. Biol. 66(4–5) (2013) 743–766] to describe the effect on biological invasions of networks with fast diffusion imbedded in a field. Here we study the eigenvalue associated with heterogeneous generalizations of this model. In a forthcoming work [Influence of a line with fast diffusion on an ecological niche, preprint (2018)] we show that persistence or extinction of the associated nonlinear evolution equation is fully accounted for by this generalized eigenvalue. A key element in the proofs is a new Harnack inequality that we establish for these systems and which is of independent interest.

Structure Preserving Numerical Analysis of HIV and CD4+T-Cells Reaction Diffusion Model in Two Space Dimensions

2020 ◽  
Vol 139 ◽  
pp. 110307
Author(s):  
Nauman Ahmed ◽  
Muhammad Rafiq ◽  
Waleed Adel ◽  
Hadi Rezazadeh ◽  
Ilyas Khan ◽  
...  
Keyword(s):  
T Cells ◽  
Numerical Analysis ◽  
Diffusion Model ◽  
Cd4 T Cells ◽  
Reaction Diffusion ◽  
Structure Preserving ◽  
Reaction Diffusion Model ◽  
Two Space Dimensions

scholarly journals Numerical Analysis of the Susceptible Exposed Infected Quarantined and Vaccinated (SEIQV) Reaction-Diffusion Epidemic Model

2020 ◽  
Vol 7 ◽  
Author(s):  
Nauman Ahmed ◽  
Mehreen Fatima ◽  
Dumitru Baleanu ◽  
Kottakkaran Sooppy Nisar ◽  
Ilyas Khan ◽  
...  
Keyword(s):  
Numerical Analysis ◽  
Epidemic Model ◽  
Reaction Diffusion

Numerical analysis of a reaction–diffusion–convection system

2003 ◽  
Vol 27 (4) ◽  
pp. 579-594 ◽  
Author(s):  
Khalid Alhumaizi ◽  
Redhouane Henda ◽  
Mostafa Soliman
Keyword(s):  
Numerical Analysis ◽  
Reaction Diffusion ◽  
Diffusion Convection
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