scholarly journals Quenching Time for Some Semilinear Equations with A Potential

2019 ◽  
Vol 7 (2) ◽  
Author(s):  
Rémi K. Kouakou ◽  
Firmin K. N’gohissé
Keyword(s):  
Semilinear Equations ◽  
Quenching Time

scholarly journals Bifurcation Analysis of an Age Structured HIV Infection Model with Both Virus-to-Cell and Cell-to-Cell Transmissions

2018 ◽  
Vol 28 (09) ◽  
pp. 1850109 ◽  
Author(s):  
Xiangming Zhang ◽  
Zhihua Liu
Keyword(s):  
T Cells ◽  
Hopf Bifurcation ◽  
Hiv Infection ◽  
Bifurcation Analysis ◽  
Dynamical Behavior ◽  
Infection Model ◽  
Positive Equilibrium ◽  
Semilinear Equations ◽  
Age Structured ◽  
Hiv Infection Model

We make a mathematical analysis of an age structured HIV infection model with both virus-to-cell and cell-to-cell transmissions to understand the dynamical behavior of HIV infection in vivo. In the model, we consider the proliferation of uninfected CD[Formula: see text] T cells by a logistic function and the infected CD[Formula: see text] T cells are assumed to have an infection-age structure. Our main results concern the Hopf bifurcation of the model by using the theory of integrated semigroup and the Hopf bifurcation theory for semilinear equations with nondense domain. Bifurcation analysis indicates that there exist some parameter values such that this HIV infection model has a nontrivial periodic solution which bifurcates from the positive equilibrium. The numerical simulations are also carried out.

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