scholarly journals Local asymptotic stability of a system of integro-differential equations describing clonal evolution of a self-renewing cell population under mutation

2022 ◽  
Vol 84 (1-2) ◽  
Author(s):  
Jan-Erik Busse ◽  
Sílvia Cuadrado ◽  
Anna Marciniak-Czochra
Keyword(s):  
Asymptotic Stability ◽  
Differential Equations ◽  
Cell Population ◽  
Clonal Evolution ◽  
Local Asymptotic Stability

ASYMPTOTIC STABILITY OF EQUILIBRIUM STATES FOR AMBIPOLAR PLASMAS

2004 ◽  
Vol 14 (09) ◽  
pp. 1361-1399 ◽  
Author(s):  
V. GIOVANGIGLI ◽  
B. GRAILLE
Keyword(s):  
Partial Differential Equations ◽  
Asymptotic Stability ◽  
Differential Equations ◽  
Null Space ◽  
Current Model ◽  
Debye Length ◽  
Equilibrium States ◽  
Electron Mass ◽  
Partial Differential ◽  
Stability Of Equilibrium

We investigate a system of partial differential equations modeling ambipolar plasmas. The ambipolar — or zero current — model is obtained from general plasmas equations in the limit of vanishing Debye length. In this model, the electric field is expressed as a linear combination of macroscopic variable gradients. We establish that the governing equations can be written as a symmetric form by using entropic variables. The corresponding dissipation matrices satisfy the null space invariant property and the system of partial differential equations can be written as a normal form, i.e. in the form of a symmetric hyperbolic–parabolic composite system. By properly modifying the chemistry source terms and/or the diffusion matrices, asymptotic stability of equilibrium states is established and decay estimates are obtained. We also establish the continuous dependence of global solutions with respect to vanishing electron mass.

Local asymptotic stability for dissipative wave systems

1998 ◽  
Vol 104 (1) ◽  
pp. 29-50 ◽  
Author(s):  
Patrizia Pucci ◽  
James Serrin
Keyword(s):  
Asymptotic Stability ◽  
Local Asymptotic Stability

scholarly journals Mathematical Analysis of an Immune-structured Hikungunya Transmission Model

2019 ◽  
Vol 12 (4) ◽  
pp. 1533-1552
Author(s):  
Kambire Famane ◽  
Gouba Elisée ◽  
Tao Sadou ◽  
Blaise Some
Keyword(s):  
Numerical Simulation ◽  
Asymptotic Stability ◽  
Deterministic Model ◽  
Reproduction Number ◽  
Transmission Model ◽  
Acquired Immunity ◽  
Local Asymptotic Stability ◽  
Well Posed ◽  
Disease Free ◽  
The Basic Reproduction Number

In this paper, we have formulated a new deterministic model to describe the dynamics of the spread of chikunguya between humans and mosquitoes populations. This model takes into account the variation in mortality of humans and mosquitoes due to other causes than chikungunya disease, the decay of acquired immunity and the immune sytem boosting. From the analysis, itappears that the model is well posed from the mathematical and epidemiological standpoint. The existence of a single disease free equilibrium has been proved. An explicit formula, depending on the parameters of the model, has been obtained for the basic reproduction number R0 which is used in epidemiology. The local asymptotic stability of the disease free equilibrium has been proved. The numerical simulation of the model has confirmed the local asymptotic stability of the diseasefree equilbrium and the existence of endmic equilibrium. The varying effects of the immunity parameters has been analyzed numerically in order to provide better conditions for reducing the transmission of the disease.

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