scholarly journals A Double S-Shaped Bifurcation Curve for a Reaction-Diffusion Model with Nonlinear Boundary Conditions

2010 ◽  
Vol 2010 (1) ◽  
pp. 357542 ◽  
Author(s):  
Jerome Goddard ◽  
EunKyoung Lee ◽  
R Shivaji
Keyword(s):  
Boundary Conditions ◽  
Diffusion Model ◽  
Nonlinear Boundary ◽  
Reaction Diffusion ◽  
Nonlinear Boundary Conditions ◽  
Bifurcation Curve ◽  
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

The Phenomenon of Quenching for a Reaction-Diffusion System with Non-Linear Boundary Conditions

2021 ◽  
Vol 88 (1-2) ◽  
pp. 155
Author(s):  
Halima Nachid ◽  
F. N'Gohisse ◽  
N'Guessan Koffi
Keyword(s):  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Reaction Diffusion ◽  
Nonlinear Boundary Conditions ◽  
Reaction Diffusion System ◽  
Diffusion System ◽  
Lower And Upper Bounds ◽  
Linear Reaction ◽  
The One ◽  
Quenching Time

We study the quenching behavior of the solution of a semi- linear reaction-diffusion system with nonlinear boundary conditions. We prove that the solution quenches in finite time and its quenching time goes to the one of the solution of the differential system. We also obtain lower and upper bounds for quenching time of the solution.

scholarly journals Bifurcation from infinity for reaction–diffusion equations under nonlinear boundary conditions

2017 ◽  
Vol 147 (3) ◽  
pp. 649-671
Author(s):  
Nsoki Mavinga ◽  
Rosa Pardo
Keyword(s):  
Maximum Principle ◽  
Boundary Conditions ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Reaction Diffusion ◽  
Nonlinear Boundary Conditions ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Asymptotically Linear ◽  
Bifurcation From Infinity

We consider reaction–diffusion equations under nonlinear boundary conditions where the nonlinearities are asymptotically linear at infinity and depend on a parameter. We prove that, as the parameter crosses some critical values, a resonance-type phenomenon provides solutions that bifurcate from infinity. We characterize the bifurcated branches when they are sub- or supercritical. We obtain both Landesman–Lazer-type conditions that guarantee the existence of solutions in the resonant case and an anti-maximum principle.

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