Long time behavior of solutions of a diffusion–advection logistic model with free boundaries

2014 ◽  
Vol 37 ◽  
pp. 49-53 ◽  
Author(s):  
Hong Gu ◽  
Zhigui Lin ◽  
Bendong Lou
Keyword(s):  
Logistic Model ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Free Boundaries ◽  
Long Time

scholarly journals $m$th-order Fisher-KPP equation with free boundaries and time-aperiodic advection

2021 ◽  
Author(s):  
Changqing Ji ◽  
Dandan Zhu ◽  
Jingli Ren
Keyword(s):  
Large Amplitude ◽  
Small Amplitude ◽  
Initial Conditions ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Free Boundaries ◽  
Kpp Equation ◽  
Advection Term ◽  
Long Time ◽  
Theoretical Results

In this paper, we investigate a $m$th-order Fisher-KPP equation with free boundaries and time-aperiodic advection. Considering the influence of advection term and initial conditions on the long time behavior of solutions, we obtain spreading-vanishing dichotomy, spreading-transition-vanishing trichotomy, and vanishing happens with the coefficient of advection term in small amplitude, medium-sized amplitude and large amplitude, respectively. Then, the appropriate parameters are selected in the simulation to intuitively show the corresponding theoretical results. Moreover, the wave-spreading and wave-vanishing cases of the solutions are observed in our study.

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.

Sign in / Sign up

Export Citation Format

Share Document