Uniform boundedness and stability of global solutions in a strongly coupled three-species cooperating model

2008 ◽  
Vol 9 (2) ◽  
pp. 272-289 ◽  
Author(s):  
Shengmao Fu ◽  
Zijuan Wen ◽  
Shangbin Cui
Keyword(s):  
Uniform Boundedness ◽  
Global Solutions ◽  
Strongly Coupled

scholarly journals Global Behavior for a Strongly Coupled Predator-Prey Model with One Resource and Two Consumers

2012 ◽  
Vol 2012 ◽  
pp. 1-25
Author(s):  
Yujuan Jiao ◽  
Shengmao Fu
Keyword(s):  
Functional Response ◽  
Sufficient Conditions ◽  
Uniform Boundedness ◽  
Global Solutions ◽  
Energy Estimates ◽  
Positive Equilibrium ◽  
Strongly Coupled ◽  
Predator Prey ◽  
Predator Prey Model ◽  
Prey Model

We consider a strongly coupled predator-prey model with one resource and two consumers, in which the first consumer species feeds on the resource according to the Holling II functional response, while the second consumer species feeds on the resource following the Beddington-DeAngelis functional response, and they compete for the common resource. Using the energy estimates and Gagliardo-Nirenberg-type inequalities, the existence and uniform boundedness of global solutions for the model are proved. Meanwhile, the sufficient conditions for global asymptotic stability of the positive equilibrium for this model are given by constructing a Lyapunov function.

scholarly journals Existence of global solutions for the Shigesada-Kawasaki-Teramoto model with strongly coupled cross-diffusion

2004 ◽  
Vol 10 (3) ◽  
pp. 719-730 ◽  
Author(s):  
Y. S. Choi ◽  
◽  
Roger Lui ◽  
Yoshio Yamada ◽  
◽  
...  
Keyword(s):  
Global Solutions ◽  
Strongly Coupled ◽  
Cross Diffusion

scholarly journals The 3D Navier–Stokes Equations: Invariants, Local and Global Solutions

Axioms ◽  
2019 ◽  
Vol 8 (2) ◽  
pp. 41 ◽  
Author(s):  
Vladimir Semenov
Keyword(s):  
Vector Fields ◽  
Stokes Equations ◽  
Uniform Boundedness ◽  
Global Solutions ◽  
Navier Stokes ◽  
Solenoidal Vector ◽  
Navier Stokes Equations ◽  
Scaling Procedure ◽  
Sufficient And Necessary Conditions ◽  
Special Invariant

In this article, I consider local solutions of the 3D Navier–Stokes equations and its properties such as an existence of global and smooth solution, uniform boundedness. The basic role is assigned to a special invariant class of solenoidal vector fields and three parameters that are invariant with respect to the scaling procedure. Since in spaces of even dimensions the scaling procedure is a conformal mapping on the Heisenberg group, then an application of invariant parameters can be considered as the application of conformal invariants. It gives the possibility to prove the sufficient and necessary conditions for existence of a global regular solution. This is the main result and one among some new statements. With some compliments, the rest improves well-known classical results.

scholarly journals Global solution of reaction diusion system with full matrix

2015 ◽  
Vol 3 (3) ◽  
pp. 109
Author(s):  
Mebarki Maroua ◽  
Moumeni Abdelkader
Keyword(s):  
Global Existence ◽  
Wide Class ◽  
Diffusion Coefficients ◽  
Lyapunov Functional ◽  
Global Solutions ◽  
Reaction Diffusion ◽  
Strongly Coupled ◽  
Full Matrix ◽  
Functional Methods ◽  
Coupled Reaction

<p>The purpose of this paper is to prove the global existence in time of solutions for the strongly coupled reaction-diffusion system:</p><p><img src="/public/site/images/admin/Capture.JPG" alt="" /><br /><br />with full matrix of diffusion coefficients. Our techniques of proof are based on Lyapunov functional methods and some \(L^{p}\) estimates. we show that global solutions exist. Our investigation applied for a wide class of the nonlinear terms <em>f</em> and <em>g</em>.</p>

Global Solutions of a Diffusive Predator-Prey Model with Holling IV Functional Response

2013 ◽  
Vol 336-338 ◽  
pp. 664-667
Author(s):  
Yu Juan Jiao
Keyword(s):  
Functional Response ◽  
Existence Of Solutions ◽  
Uniform Boundedness ◽  
Global Solutions ◽  
Energy Estimates ◽  
Predator Prey ◽  
Cross Diffusion ◽  
Predator Prey Model ◽  
Global Existence Of Solutions ◽  
Prey Model

Using the energy estimates and Gagliardo-Nirenberg type inequalities, the uniform boundedness and global existence of solutions for a predator-prey model with Holling IV functional response with self- and cross-diffusion are proved.

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