Entire solutions for some reaction–diffusion systems

2015 ◽  
Vol 08 (04) ◽  
pp. 1550052 ◽  
Author(s):  
Guangying Lv ◽  
Dang Luo
Keyword(s):  
Classical Solution ◽  
General Model ◽  
Reaction Diffusion ◽  
Entire Solution ◽  
Reaction Model ◽  
Entire Solutions ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Time Variables ◽  
Belousov Zhabotinskii Reaction

This paper is concerned with the existence of entire solutions of some reaction–diffusion systems. We first consider Belousov–Zhabotinskii reaction model. Then we study a general model. Using the comparing argument and sub-super-solutions method, we obtain the existence of entire solutions which behave as two wavefronts coming from the both sides of x-axis, where an entire solution is meant by a classical solution defined for all space and time variables. At last, we give some examples to explain our results for the general models.

scholarly journals Global Existence of Solutions to a Class of Reaction–Diffusion Systems on Rn

2021 ◽  
Author(s):  
Salah Badraoui
Keyword(s):  
Initial Data ◽  
Global Existence ◽  
Classical Solution ◽  
Space Dimension ◽  
Existence Of Solutions ◽  
Bounded Function ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Global Existence Of Solutions ◽  
Diffusion Systems

We prove in this work the existence of a unique global nonnegative classical solution to the class of reaction–diffusion systems uttx=aΔutx−guvm,vttx=dΔvtx+λtxguvm, where a>0, d>0, t>0,x∈Rn, n,m∈N∗, λ is a nonnegative bounded function with λt.∈BUCRn for all t∈R+, the initial data u0, v0∈BUCRn, g:BUCRn→BUCRn is a of class C1,dgudu∈L∞R, g0=0 and gu≥0 for all u≥0. The ideas of the proof is inspired from the work of Collet and Xin who proved the same result in the particular case d>a=1, λ=1,gu=u. Moreover, they showed that the L∞-norm of v can not grow faster than Olnlnt for any space dimension.

ENTIRE SOLUTIONS FOR LOTKA–VOLTERRA COMPETITION-DIFFUSION MODEL

2013 ◽  
Vol 06 (04) ◽  
pp. 1350020 ◽  
Author(s):  
XIAOHUAN WANG ◽  
GUANGYING LV
Keyword(s):  
Classical Solution ◽  
Diffusion Model ◽  
Entire Solution ◽  
Entire Solutions ◽  
Wave Fronts ◽  
Space And Time ◽  
Time Variables ◽  
Competition Diffusion

This paper is concerned with the existence of entire solutions of Lotka–Volterra competition-diffusion model. Using the comparing argument and sub-super solutions method, we obtain the existence of entire solutions which behave as two wave fronts coming from the both sides of x-axis, where an entire solution is meant by a classical solution defined for all space and time variables.

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