scholarly journals Global existence and blow-up problems for reaction diffusion model with multiple nonlinearities

2008 ◽  
Vol 343 (1) ◽  
pp. 159-169 ◽  
Author(s):  
Juntang Ding ◽  
Xuyan Gao ◽  
Shengjia Li
Keyword(s):  
Global Existence ◽  
Diffusion Model ◽  
Blow Up ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model

scholarly journals CRITICAL EXPONENTS FOR A REACTION–DIFFUSION MODEL WITH ABSORPTIONS AND COUPLED BOUNDARY FLUX

2005 ◽  
Vol 48 (1) ◽  
pp. 241-252 ◽  
Author(s):  
Sining Zheng ◽  
Fengjie Li
Keyword(s):  
Diffusion Model ◽  
Critical Exponents ◽  
Nonlinear Boundary ◽  
Blow Up ◽  
Reaction Diffusion ◽  
Nonlinear Boundary Conditions ◽  
Reaction Diffusion Model ◽  
Precise Analysis ◽  
Two Parameters ◽  
Boundary Flux

AbstractThis paper deals with a reaction–diffusion model with inner absorptions and coupled nonlinear boundary conditions of exponential type. The critical exponents are described via a pair of parameters that satisfy a certain matrix equation containing all the six nonlinear exponents of the system. Whether the solutions blow up or not is determined by the signs of the two parameters. A more precise analysis, depending on the geometry of $\varOmega$ and the absorption coefficients, is proposed for the critical sign of the parameters.AMS 2000 Mathematics subject classification: Primary 35K55; 35B33

Asymptotic behaviour, uniqueness and stability of coexistence states of a non-cooperative reaction–diffusion model of nuclear reactors

2010 ◽  
Vol 140 (1) ◽  
pp. 189-201 ◽  
Author(s):  
Rui Peng ◽  
Dong Wei ◽  
Guoying Yang
Keyword(s):  
Asymptotic Behaviour ◽  
Diffusion Model ◽  
Blow Up ◽  
Nuclear Reactors ◽  
Reaction Diffusion ◽  
Fast Neutrons ◽  
Fuel Temperature ◽  
Reaction Diffusion Model ◽  
Coexistence States ◽  
Spatial Dimensions

We investigate a non-cooperative reaction-diffusion model arising in the theory of nuclear reactors and are concerned with the associated steady-state problem. We determine the asymptotic behaviour of the coexistence states near the point of bifurcation from infinity, which exhibits the following very interesting spatial blow-up pattern: when the fuel temperature reaches a certain value, the free fast neutrons undergoing nuclear reaction will blow up in each spatial point of the interior of the reactor. Without any restriction on spatial dimensions, we also discuss the uniqueness and stability of the coexistence states. Our results complement and sharpen those derived in two recent works by Arioli and Lóopez-Gómez.

scholarly journals A new analyzing technique for nonlinear time fractional Cauchy reaction-diffusion model equations

2020 ◽  
Vol 19 ◽  
pp. 103462 ◽  
Author(s):  
Hijaz Ahmad ◽  
Tufail A. Khan ◽  
Imtiaz Ahmad ◽  
Predrag S. Stanimirović ◽  
Yu-Ming Chu
Keyword(s):  
Diffusion Model ◽  
Reaction Diffusion ◽  
Reaction Diffusion Model ◽  
Model Equations
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