Contrast Structures in Problems for a Stationary Equation of Reaction-Diffusion-Advection Type with Discontinuous Nonlinearity

2018 ◽  
Vol 104 (5-6) ◽  
pp. 735-744 ◽  
Author(s):  
Yafei Pan ◽  
Mingkang Ni ◽  
M. A. Davydova
Keyword(s):  
Reaction Diffusion ◽  
Discontinuous Nonlinearity ◽  
Stationary Equation ◽  
Contrast Structures

scholarly journals DYNAMICS OF A REACTION–DIFFUSION EQUATION WITH A DISCONTINUOUS NONLINEARITY

2006 ◽  
Vol 16 (10) ◽  
pp. 2965-2984 ◽  
Author(s):  
JOSÉ M. ARRIETA ◽  
ANÍBAL RODRÍGUEZ-BERNAL ◽  
JOSÉ VALERO
Keyword(s):  
Nonlinear Dynamics ◽  
Diffusion Equation ◽  
Fixed Points ◽  
Global Attractor ◽  
Nonlinear Term ◽  
Upper Semicontinuity ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equation ◽  
Discontinuous Nonlinearity ◽  
Smooth Approximations

We study the nonlinear dynamics of a reaction–diffusion equation where the nonlinearity presents a discontinuity. We prove the upper semicontinuity of solutions and the global attractor with respect to smooth approximations of the nonlinear term. We also give a complete description of the set of fixed points and study their stability. Finally, we analyze the existence of heteroclinic connections between the fixed points, obtaining information on the fine structure of the global attractor.

Sign in / Sign up

Export Citation Format

Share Document