scholarly journals Anti-periodic problem for semilinear differential inclusions involving Hille-Yosida operators

2021 ◽  
pp. 1-31
Author(s):  
Nguyen Thi Van Anh ◽  
Tran Dinh Ke ◽  
Do Lan
Keyword(s):  
Periodic Solutions ◽  
Differential Inclusions ◽  
Mild Solutions ◽  
Periodic Problem ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Multivalued Maps ◽  
Integrated Semigroups ◽  
Long Time ◽  
Theoretical Results

In this paper we are interested in the anti-periodic problem governed by a class of semilinear differential inclusions with linear parts generating integrated semigroups. By adopting the Lyapunov-Perron method and the fixed point argument for multivalued maps, we prove the existence of anti-periodic solutions. Furthermore, we study the long-time behavior of mild solutions in connection with anti-periodic solutions. Consequently, as the nonlinearity is of single-valued, we obtain the exponential stability of anti-periodic solutions. An application of theoretical results to a class of partial differential equations will be given.

The asymptotic behavior of a stochastic multigroup SIS model

2018 ◽  
Vol 11 (03) ◽  
pp. 1850037 ◽  
Author(s):  
Chunyan Ji ◽  
Daqing Jiang
Keyword(s):  
Asymptotic Behavior ◽  
Numerical Simulations ◽  
Stationary Distribution ◽  
Endemic Equilibrium ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Sis Model ◽  
Stochastic Perturbations ◽  
Long Time ◽  
Theoretical Results

In this paper, we explore the long time behavior of a multigroup Susceptible–Infected–Susceptible (SIS) model with stochastic perturbations. The conditions for the disease to die out are obtained. Besides, we also show that the disease is fluctuating around the endemic equilibrium under some conditions. Moreover, there is a stationary distribution under stronger conditions. At last, some numerical simulations are applied to support our theoretical results.

scholarly journals Long-Time Behavior of Solution for a Reactor Model

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Yantao Guo ◽  
Jianwei Shen ◽  
Qianqian Zheng
Keyword(s):  
Weak Solution ◽  
Numerical Experiments ◽  
Measure Of Noncompactness ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Reactor Model ◽  
Kuratowski Measure Of Noncompactness ◽  
Dynamical Behaviors ◽  
Long Time ◽  
Theoretical Results

In this paper, we would consider the dynamical behaviors of the chemical model represented by Satnoianu et al. (2001). Using the Kuratowski measure of noncompactness method, we prove the existence of global attractor for the weak solution semiflow of system. Finally, several numerical experiments confirm the theoretical results.

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 Study of the dynamics of two chemostats connected by Fickian diffusion with bounded random fluctuations

2021 ◽  
Author(s):  
Tomás Caraballo ◽  
Javier López-de-la-Cruz ◽  
Alain Rapaport
Keyword(s):  
Numerical Simulations ◽  
Existence And Uniqueness ◽  
Fickian Diffusion ◽  
Time Behavior ◽  
Long Time Behavior ◽  
State Variables ◽  
Random System ◽  
Long Time ◽  
Random Fluctuations ◽  
Theoretical Results

This paper investigates the dynamics of a model of two chemostats connected by Fickian diffusion with bounded random fluctuations. We prove the existence and uniqueness of non-negative global solution as well as the existence of compact absorbing and attracting sets for the solutions of the corresponding random system. After that, we study the internal structure of the attracting set to obtain more detailed information about the long-time behavior of the state variables. In such a way, we provide conditions under which the extinction of the species cannot be avoided and conditions to ensure the persistence of the species, which is often the main goal pursued by practitioners. In addition, we illustrate the theoretical results with several numerical simulations.

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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