Asymptotic behavior of solutions for a free boundary problem with a nonlinear gradient absorption

2019 ◽  
Vol 58 (1) ◽  
Author(s):  
Zhengce Zhang ◽  
Xiangli Zhang
Keyword(s):  
Asymptotic Behavior ◽  
Free Boundary ◽  
Boundary Problem ◽  
Free Boundary Problem ◽  
Asymptotic Behavior Of Solutions ◽  
A Free Boundary Problem

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).

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