A class of nonlinear singularly perturbed nonlocal reaction diffusion system

2003 ◽  
Vol 18 (4) ◽  
pp. 403-411
Author(s):  
Mo Jiaqi
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Singularly Perturbed ◽  
Diffusion System ◽  
Nonlocal Reaction

THE SINGULARLY PERTURBED NONLOCAL REACTION DIFFUSION SYSTEM

2002 ◽  
Vol 22 (4) ◽  
pp. 549-556 ◽  
Author(s):  
Jiaqi Mo ◽  
Xianglin Han ◽  
Songlin Chen
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Singularly Perturbed ◽  
Diffusion System ◽  
Nonlocal Reaction

Pulses and global bifurcations in a nonlocal reaction-diffusion system

1993 ◽  
Vol 48 (4) ◽  
pp. 2917-2923 ◽  
Author(s):  
Michael D. Graham ◽  
Usuf Middya ◽  
Dan Luss
Keyword(s):  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Global Bifurcations ◽  
Nonlocal Reaction

Global existence and blow-up of solutions to a nonlocal reaction-diffusion system

2003 ◽  
Vol 9 (6) ◽  
pp. 1519-1532 ◽  
Author(s):  
Shu-Xiang Huang ◽  
◽  
Fu-Cai Li ◽  
Chun-Hong Xie ◽  
Keyword(s):  
Global Existence ◽  
Blow Up ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Nonlocal Reaction

scholarly journals THE EXISTENCE AND UNIQUENESS OF THE MILD SOLUTION TO A NONLINEAR CAUCHY PROBLEM ASSOCIATED WITH A NONLOCAL REACTION-DIFFUSION SYSTEM

2019 ◽  
Vol 11 (2) ◽  
pp. 19
Author(s):  
Bambang Hendriya Guswanto ◽  
Mohd. Ariff Bin Admon ◽  
Nur Natasha Binti Lim Boon Chye
Keyword(s):  
Cauchy Problem ◽  
Mild Solution ◽  
Existence And Uniqueness ◽  
Linear Part ◽  
Reaction Diffusion ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Banach Fixed Point Theorem ◽  
Nonlinear Part ◽  
Nonlocal Reaction

We study the existence and uniqueness of a mild solution to a nonlinear Cauchy problem associated with a nonlocal reaction diffusion system by employing the properties of analytic semigroup operator generated by the linear part of the problem which is sectorial and then applying Banach Fixed Point Theorem to the problem. We show that the problem has a unique mild solution under a Lipschitz condition on the nonlinear part of the problem. An example as an application of the result obtained is also given.

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