Asymptotic behavior and global existence of solutions to a two-species chemotaxis system with two chemicals

2018 ◽  
Vol 69 (4) ◽  
Author(s):  
E. Cruz ◽  
M. Negreanu ◽  
J. I. Tello
Keyword(s):  
Asymptotic Behavior ◽  
Global Existence ◽  
Existence Of Solutions ◽  
Global Existence Of Solutions ◽  
Chemotaxis System

GLOBAL EXISTENCE TO THE EINSTEIN-SCALAR FIELD SYSTEM ON THE ROBERTSON–WALKER SPACE-TIMES WITH HYPERBOLIC AND SPHERICAL SYMMETRIES

2010 ◽  
Vol 07 (01) ◽  
pp. 69-83
Author(s):  
NORBERT NOUTCHEGUEME ◽  
ALEXIS NANGUE
Keyword(s):  
Asymptotic Behavior ◽  
Scalar Field ◽  
Global Existence ◽  
Initial Velocity ◽  
Existence Of Solutions ◽  
Expansion Factor ◽  
Positive Cosmological Constant ◽  
Field System ◽  
Global Existence Of Solutions ◽  
Cosmological Expansion

Global existence of solutions is proved and asymptotic behavior is investigated, in the case of a positive cosmological constant and positive initial velocity of the cosmological expansion factor.

scholarly journals Blow-up and global existence for a kinetic equation of swarm formation

2017 ◽  
Vol 27 (06) ◽  
pp. 1153-1175 ◽  
Author(s):  
Mirosław Lachowicz ◽  
Henryk Leszczyński ◽  
Martin Parisot
Keyword(s):  
Asymptotic Behavior ◽  
Kinetic Equation ◽  
Global Existence ◽  
Integral Operator ◽  
Blow Up ◽  
Existence Of Solutions ◽  
Interaction Rate ◽  
Global Existence Of Solutions ◽  
Nonlinear Integral Operator ◽  
The Right

In this paper we study a kinetic equation that describes swarm formations. The right-hand side of this equation contains nonlinear integro-differential terms responsible for two opposite tendencies: dissipation and swarming. The nonlinear integral operator describes the changes of velocities (orientations) of interacting individuals. The interaction rate is assumed to be dependent of velocities of interacting individuals. Although the equation seems to be rather simple it leads to very complicated dynamics. In this paper, we study possible blow-ups versus global existence of solutions and provide results on the asymptotic behavior. The complicated dynamics and possibility of blow-ups can be directly related to creation of swarms.

scholarly journals Global existence of solutions to parabolic two species predator-prey chemotaxis system

2021 ◽  
Author(s):  
Arumugam Gurusamy ◽  
Gnanasekaran Shanmugasundaram ◽  
Nithyadevi nagarajan ◽  
Yang He
Keyword(s):  
Global Existence ◽  
Existence Of Solutions ◽  
Predator Prey ◽  
Global Existence Of Solutions ◽  
Chemotaxis System
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