scholarly journals Boundedness and Large-Time Behavior Results for a Diffusive Epidemic Model

2007 ◽  
Vol 2007 ◽  
pp. 1-15 ◽  
Author(s):  
Lamine Melkemi ◽  
Ahmed Zerrouk Mokrane ◽  
Amar Youkana
Keyword(s):  
Asymptotic Behavior ◽  
Large Time ◽  
System Modeling ◽  
Uniform Boundedness ◽  
Reaction Diffusion ◽  
Large Time Behavior ◽  
Positive Answer ◽  
Time Behavior ◽  
Epidemic Disease ◽  
Infection Disease

We consider a reaction-diffusion system modeling the spread of an epidemic disease within a population divided into the susceptible and infective classes. We first consider the question of the uniform boundedness of the solutions for which we give a positive answer. Then we deal with the asymptotic behavior of the solutions where in particular we are interested in reasonable conditions leading to the extinction of the infection disease as the time goes to infinity.

Global existence and large time behavior of solutions of a time fractional reaction diffusion system

2020 ◽  
Vol 23 (2) ◽  
pp. 390-407
Author(s):  
Ahmed Alsaedi ◽  
Bashir Ahmad ◽  
Mokhtar Kirane ◽  
Rafika Lassoued
Keyword(s):  
Global Existence ◽  
Large Time ◽  
Reaction Diffusion ◽  
Large Time Behavior ◽  
Positive Answer ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Time Behavior ◽  
Feedback Method ◽  
Fractional Reaction

AbstractIn this paper, it is proved that a time fractional reaction diffusion system with reaction terms of the Brusselator type admits a global solution by using the feedback method of F. Rothe [20]. Furthermore, some results on the large time behavior of the solutions are obtained. We give a positive answer to Problem 6 of the valuable paper of Gal and Warma [6].

scholarly journals Asymptotic Behavior of Solutions to Reaction-Diffusion Equations with Dynamic Boundary Conditions and Irregular Data

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Yonghong Duan ◽  
Chunlei Hu ◽  
Xiaojuan Chai
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Conditions ◽  
Reaction Diffusion ◽  
Large Time Behavior ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary

This paper is concerned with the asymptotic behavior of solutions to reaction-diffusion equations with dynamic boundary conditions as well as L1-initial data and forcing terms. We first prove the existence and uniqueness of an entropy solution by smoothing approximations. Then we consider the large-time behavior of the solution. The existence of a global attractor for the solution semigroup is obtained in L1(Ω¯,dν). This extends the corresponding results in the literatures.

scholarly journals Asymptotic Behavior of Solutions to Fast Diffusive Non-Newtonian Filtration Equations Coupled by Nonlinear Boundary Sources

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Wang Zejia ◽  
Wang Shunti ◽  
Zhang Chengbin
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Nonlinear Boundary ◽  
Large Time ◽  
Large Time Behavior ◽  
Asymptotic Behavior Of Solutions ◽  
Time Behavior ◽  
Multidimensional Problem ◽  
Critical Curves

This paper is concerning the asymptotic behavior of solutions to the fast diffusive non-Newtonian filtration equations coupled by the nonlinear boundary sources. We are interested in the critical global existence curve and the critical Fujita curve, which are used to describe the large-time behavior of solutions. It is shown that the above two critical curves are both the same for the multidimensional problem we considered.

scholarly journals Boundedness and asymptotic behavior in a predator-prey model with indirect pursuit-evasion interaction

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Chao Liu ◽  
Bin Liu
Keyword(s):  
Asymptotic Behavior ◽  
Large Time ◽  
Neumann Boundary ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Smooth Bounded Domain ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Pursuit Evasion ◽  
Predator Model

<p style='text-indent:20px;'>In this paper, we study the prey-predator model with indirect pursuit-evasion interaction defined on a smooth bounded domain with homogeneous Neumann boundary conditions. We obtain the globa existence and boundedness of the classical solution of the model by estimating <inline-formula><tex-math id="M1">\begin{document}$ L^{p} $\end{document}</tex-math></inline-formula>-norm of <inline-formula><tex-math id="M2">\begin{document}$ u $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M3">\begin{document}$ v $\end{document}</tex-math></inline-formula>, and we also show the large time behavior and convergence rate of the solution.</p>

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