scholarly journals Influence of Flux Limitation on Large Time Behavior in a Three-Dimensional Chemotaxis-Stokes System Modeling Coral Fertilization

2021 ◽  
Vol 174 (1) ◽  
Author(s):  
Ji Liu
Keyword(s):  
Stokes System ◽  
Large Time ◽  
System Modeling ◽  
Three Dimensional ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Flux Limitation

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.

scholarly journals On $ L^1 $ estimates of solutions of compressible viscoelastic system

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yusuke Ishigaki
Keyword(s):  
Initial Data ◽  
Large Time ◽  
Three Dimensional ◽  
Large Time Behavior ◽  
Time Behavior ◽  
Viscoelastic System ◽  
Diffusion Wave ◽  
Estimates Of Solutions ◽  
Whole Space ◽  
Wave Phenomena

<p style='text-indent:20px;'>We consider the large time behavior of solutions of compressible viscoelastic system around a motionless state in a three-dimensional whole space. We show that if the initial data belongs to <inline-formula><tex-math id="M2">\begin{document}$ W^{2,1} $\end{document}</tex-math></inline-formula>, and is sufficiently small in <inline-formula><tex-math id="M3">\begin{document}$ H^4\cap L^1 $\end{document}</tex-math></inline-formula>, the solutions grow in time at the same rate as <inline-formula><tex-math id="M4">\begin{document}$ t^{\frac{1}{2}} $\end{document}</tex-math></inline-formula> in <inline-formula><tex-math id="M5">\begin{document}$ L^1 $\end{document}</tex-math></inline-formula> due to diffusion wave phenomena of the system caused by interaction between sound wave, viscous diffusion and elastic wave.</p>

scholarly journals Large Time Behavior for Weak Solutions of the 3D Globally Modified Navier-Stokes Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Junbai Ren
Keyword(s):  
Weak Solutions ◽  
Large Time ◽  
Stokes Equations ◽  
Three Dimensional ◽  
Large Time Behavior ◽  
Navier Stokes ◽  
Heat Semigroup ◽  
Time Behavior ◽  
Decay Estimates ◽  
Navier Stokes Equations

This paper is concerned with the large time behavior of the weak solutions for three-dimensional globally modified Navier-Stokes equations. With the aid of energy methods and auxiliary decay estimates together withLp-Lqestimates of heat semigroup, we derive the optimal upper and lower decay estimates of the weak solutions for the globally modified Navier-Stokes equations asC1(1+t)-3/4≤uL2≤C2(1+t)-3/4,  t>1.The decay rate is optimal since it coincides with that of heat equation.

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