A reaction-diffusion-advection competition model with a free boundary

2021 ◽  
Vol 65 (3) ◽  
pp. 25-37
Keyword(s):  
Free Boundary ◽  
A Priori Estimates ◽  
A Priori ◽  
Reaction Diffusion ◽  
Competition Model ◽  
Baseline Data ◽  
The Other ◽  
Quasilinear System ◽  
Priori Estimates ◽  
Competitive Diffusion

In this paper, we study a competitive diffusion quasilinear system with a free boundary. First, we investigate the mathematical questions of the problem. A priori estimates of Schauder type are established, which are necessary for the solvability of the problem. One of two competing species is an invader, which initially exists on a certain sub-interval. The other is initially distributed throughout the area under consideration. Examining the influence of baseline data on the success or failure of the first invasion. We conclude that there is a dichotomy of spread and extinction and give precise criteria for spread and extinction in this model.

Existence of bistable waves for a nonlocal and nonmonotone reaction-diffusion equation

2019 ◽  
Vol 150 (2) ◽  
pp. 721-739
Author(s):  
Sergei Trofimchuk ◽  
Vitaly Volpert
Keyword(s):  
Diffusion Equation ◽  
A Priori Estimates ◽  
Travelling Waves ◽  
A Priori ◽  
Unbounded Domains ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Nonlocal Nonlinearity ◽  
Estimates Of Solutions ◽  
Priori Estimates

AbstractReaction-diffusion equation with a bistable nonlocal nonlinearity is considered in the case where the reaction term is not quasi-monotone. For this equation, the existence of travelling waves is proved by the Leray-Schauder method based on the topological degree for elliptic operators in unbounded domains and a priori estimates of solutions in properly chosen weighted spaces.

scholarly journals A priori estimates for the 3D compressible free-boundary Euler equations with surface tension in the case of a liquid

2019 ◽  
Vol 8 (3) ◽  
pp. 503-542 ◽  
Author(s):  
Marcelo M. Disconzi ◽  
◽  
Igor Kukavica ◽  
Keyword(s):  
Surface Tension ◽  
Free Boundary ◽  
Euler Equations ◽  
A Priori Estimates ◽  
A Priori ◽  
Priori Estimates

scholarly journals On the Sirs Epidemic Model with Free Boundaries

2021 ◽  
Vol 66 (1) ◽  
pp. 21-47
Author(s):  
J. O. Takhirov ◽  
◽  
Z. K. Djumanazarova ◽  
Keyword(s):  
A Priori Estimates ◽  
A Priori ◽  
Sufficient Conditions ◽  
Reaction Diffusion ◽  
Global Solvability ◽  
Reproductive Number ◽  
Free Boundaries ◽  
Sirs Epidemic Model ◽  
Priori Estimates ◽  
Initial Area

We investigate an epidemic non-linear reaction-diffusion system with two free boundaries. A free boundary is introduced to describe the expanding front of the infectious environment. A priori estimates of the required functions are established, which are necessary for the correctness and global solvability of the problem. We get sufficient conditions for the spread or disappearance of the disease. It has been proven that with a base reproductive number the disease disappears in the long term if the initial values and the initial area are sufficiently small.

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