scholarly journals A simple system of reaction-diffusion equations describing morphogenesis: Asymptotic behavior

1979 ◽  
Vol 122 (1) ◽  
pp. 141-157 ◽  
Author(s):  
F. Rothe ◽  
P. de Morttoni
Keyword(s):  
Asymptotic Behavior ◽  
Reaction Diffusion ◽  
Reaction Diffusion Equations ◽  
Simple System ◽  
Diffusion Equations

scholarly journals Asymptotic Behavior of Solutions to Reaction-Diffusion Equations with Dynamic Boundary Conditions and Irregular Data

2018 ◽  
Vol 2018 ◽  
pp. 1-13
Author(s):  
Yonghong Duan ◽  
Chunlei Hu ◽  
Xiaojuan Chai
Keyword(s):  
Asymptotic Behavior ◽  
Boundary Conditions ◽  
Reaction Diffusion ◽  
Large Time Behavior ◽  
Reaction Diffusion Equations ◽  
Diffusion Equations ◽  
Asymptotic Behavior Of Solutions ◽  
Time Behavior ◽  
Dynamic Boundary Conditions ◽  
Dynamic Boundary

This paper is concerned with the asymptotic behavior of solutions to reaction-diffusion equations with dynamic boundary conditions as well as L1-initial data and forcing terms. We first prove the existence and uniqueness of an entropy solution by smoothing approximations. Then we consider the large-time behavior of the solution. The existence of a global attractor for the solution semigroup is obtained in L1(Ω¯,dν). This extends the corresponding results in the literatures.

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