scholarly journals Long-time behavior and Darwinian optimality for an asymmetric size-structured branching process

2021 ◽  
Vol 83 (6-7) ◽  
Author(s):  
Bertrand Cloez ◽  
Benoîte de Saporta ◽  
Tristan Roget
Keyword(s):  
Branching Process ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Long Time

A multilevel branching model

1991 ◽  
Vol 23 (4) ◽  
pp. 701-715 ◽  
Author(s):  
D. A. Dawson ◽  
K. J. Hochberg
Keyword(s):  
Branching Process ◽  
Total Population ◽  
Asymptotic Expression ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Information Unit ◽  
Branching Model ◽  
State Approximation ◽  
Continuous State ◽  
Long Time

We consider a dynamic multilevel population or information system. At each level individuals or information units undergo a Galton–Watson-type branching process in which they can be replicated or removed. In addition, a collection of individuals or information units at a given level constitutes an information unit at the next higher level. Each collection of units also undergoes a Galton–Watson branching process, either dying or replicating. In this paper, we represent this multilevel branching model as a measure-valued stochastic process, study its moment structure, identify the limiting continuous-state approximation and analyse the long-time behavior in both non-critical and critical cases. For example, we obtain an asymptotic expression for the extinction probability for the total population mass process and an analogue of Yaglom's conditioned limit theorem in the critical case.

A multilevel branching model

1991 ◽  
Vol 23 (04) ◽  
pp. 701-715 ◽  
Author(s):  
D. A. Dawson ◽  
K. J. Hochberg
Keyword(s):  
Branching Process ◽  
Total Population ◽  
Asymptotic Expression ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Information Unit ◽  
Branching Model ◽  
State Approximation ◽  
Continuous State ◽  
Long Time

We consider a dynamic multilevel population or information system. At each level individuals or information units undergo a Galton–Watson-type branching process in which they can be replicated or removed. In addition, a collection of individuals or information units at a given level constitutes an information unit at the next higher level. Each collection of units also undergoes a Galton–Watson branching process, either dying or replicating. In this paper, we represent this multilevel branching model as a measure-valued stochastic process, study its moment structure, identify the limiting continuous-state approximation and analyse the long-time behavior in both non-critical and critical cases. For example, we obtain an asymptotic expression for the extinction probability for the total population mass process and an analogue of Yaglom's conditioned limit theorem in the critical case.

scholarly journals On global dynamics of 2D convective Cahn–Hilliard equation

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Initial Boundary ◽  
Initial Boundary Value Problem ◽  
Global Dynamics ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Initial Value ◽  
Hilliard Equation ◽  
Long Time ◽  
Cahn Hilliard Equation ◽  
Initial Boundary Value

AbstractIn this paper, we study the long time behavior of solution for the initial-boundary value problem of convective Cahn–Hilliard equation in a 2D case. We show that the equation has a global attractor in $H^{4}(\Omega )$ H 4 ( Ω ) when the initial value belongs to $H^{1}(\Omega )$ H 1 ( Ω ) .

The coupled Cahn–Hilliard/Allen–Cahn system with dynamic boundary conditions

2021 ◽  
pp. 1-27
Author(s):  
Ahmad Makki ◽  
Alain Miranville ◽  
Madalina Petcu
Keyword(s):  
Fractal Dimension ◽  
Boundary Conditions ◽  
Well Posedness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Finite Dimensional ◽  
Dynamic Boundary ◽  
Long Time ◽  
Finite Fractal Dimension

In this article, we are interested in the study of the well-posedness as well as of the long time behavior, in terms of finite-dimensional attractors, of a coupled Allen–Cahn/Cahn–Hilliard system associated with dynamic boundary conditions. In particular, we prove the existence of the global attractor with finite fractal dimension.

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