scholarly journals Hydrodynamical limit for a drift-diffusion system modeling large-population dynamics

2004 ◽  
Vol 291 (2) ◽  
pp. 716-726 ◽  
Author(s):  
Juan Nieto
Keyword(s):  
Population Dynamics ◽  
System Modeling ◽  
Large Population ◽  
Diffusion System ◽  
Drift Diffusion ◽  
Hydrodynamical Limit

scholarly journals On a Drift–Diffusion System for Semiconductor Devices

2016 ◽  
Vol 17 (12) ◽  
pp. 3473-3498 ◽  
Author(s):  
Rafael Granero-Belinchón
Keyword(s):  
Semiconductor Devices ◽  
Diffusion System ◽  
Drift Diffusion

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.

POPULATION DYNAMICS OF SEX-DETERMINING ALLELES IN HONEY BEES AND SELF-INCOMPATIBILITY ALLELES IN PLANTS

Genetics ◽  
1979 ◽  
Vol 91 (3) ◽  
pp. 609-626 ◽  
Author(s):  
Shozo Yokoyama ◽  
Masatoshi Nei
Keyword(s):  
Population Dynamics ◽  
Population Size ◽  
Honey Bee ◽  
Honey Bees ◽  
Finite Population ◽  
Large Population ◽  
Allele Frequencies ◽  
Self Incompatibility ◽  
Overdominant Selection ◽  
Incompatibility Alleles

ABSTRACT Mathematical theories of the population dynamics of sex-determining alleles in honey bees are developed. It is shown that in an infinitely large population the equilibrium frequency of a sex allele is l/n, where n is the number of alleles in the population, and the asymptotic rate of approach to this equilibrium is 2/(3n) per generation. Formulae for the distribution of allele frequencies and the effective and actual numbers of alleles that can be maintained in a finite population are derived by taking into account the population size and mutation rate. It is shown that the allele frequencies in a finite population may deviate considerably from l/n. Using these results, available data on the number of sex alleles in honey bee populations are discussed. It is also shown that the number of self-incompatibility alleles in plants can be studied in a much simpler way by the method used in this paper. A brief discussion about general overdominant selection is presented.

scholarly journals Uniform-in-time bounds for approximate solutions of the drift–diffusion system

2019 ◽  
Vol 141 (4) ◽  
pp. 881-916
Author(s):  
M. Bessemoulin-Chatard ◽  
C. Chainais-Hillairet
Keyword(s):  
Approximate Solutions ◽  
Diffusion System ◽  
Drift Diffusion ◽  
Time Bounds
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