scholarly journals Global existence and uniform boundedness of smooth solutions to a parabolic-parabolic chemotaxis system with nonlinear diffusion

2015 ◽  
Vol 2015 (1) ◽  
Author(s):  
Xie Li
Keyword(s):  
Global Existence ◽  
Nonlinear Diffusion ◽  
Uniform Boundedness ◽  
Smooth Solutions ◽  
Chemotaxis System

scholarly journals Global well-posedness of advective Lotka–Volterra competition systems with nonlinear diffusion

2019 ◽  
Vol 150 (5) ◽  
pp. 2322-2348
Author(s):  
Qi Wang ◽  
Jingyue Yang ◽  
Feng Yu
Keyword(s):  
Global Existence ◽  
Elliptic System ◽  
Nonlinear Diffusion ◽  
Uniform Boundedness ◽  
Parabolic Systems ◽  
Growth Conditions ◽  
Diffusion Models ◽  
Well Posedness ◽  
Sensitivity Functions ◽  
Advection Diffusion

AbstractThis paper investigates the global well-posedness of a class of reaction–advection–diffusion models with nonlinear diffusion and Lotka–Volterra dynamics. We prove the existence and uniform boundedness of the global-in-time solutions to the fully parabolic systems under certain growth conditions on the diffusion and sensitivity functions. Global existence and uniform boundedness of the corresponding parabolic–elliptic system are also obtained. Our results suggest that attraction (positive taxis) inhibits blowups in Lotka–Volterra competition systems.

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