scholarly journals Asymptotic Behavior of Solutions of Free Boundary Problem with Logistic Reaction Term

2014 ◽  
Vol 2014 ◽  
pp. 1-5
Author(s):  
Jingjing Cai
Keyword(s):  
Asymptotic Behavior ◽  
Free Boundary ◽  
Boundary Problem ◽  
Stationary Solution ◽  
Free Boundary Problem ◽  
Chemical Species ◽  
Reaction Diffusion Equation ◽  
Equation Modeling ◽  
Asymptotic Behavior Of Solutions ◽  
Bounded Interval

We study a free boundary problem for a reaction diffusion equation modeling the spreading of a biological or chemical species. In this model, the free boundary represents the spreading front of the species. We discuss the asymptotic behavior of bounded solutions and obtain a trichotomy result: spreading (the free boundary tends to+∞and the solution converges to a stationary solution defined on[0+∞)), transition (the free boundary stays in a bounded interval and the solution converges to a stationary solution with positive compact support), and vanishing (the free boundary converges to 0 and the solution tends to 0 within afinitetime).

scholarly journals Asymptotic Behavior of Solutions to Free Boundary Problem with Tresca Boundary Conditions

2021 ◽  
Vol 2021 ◽  
pp. 1-9
Author(s):  
Abdelkader Saadallah ◽  
Nadhir Chougui ◽  
Fares Yazid ◽  
Mohamed Abdalla ◽  
Bahri Belkacem Cherif ◽  
...  
Keyword(s):  
Asymptotic Behavior ◽  
Free Boundary ◽  
Boundary Conditions ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Reynolds Equation ◽  
Limit Problem ◽  
Asymptotic Behavior Of Solutions ◽  
Thin Domain

In this paper, we study the asymptotic behavior of an incompressible Herschel-Bulkley fluid in a thin domain with Tresca boundary conditions. We study the limit when the ε tends to zero, we prove the convergence of the unknowns which are the velocity and the pressure of the fluid, and we obtain the limit problem and the specific Reynolds equation.

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