scholarly journals Adaptive boundary control of constant-parameter reaction–diffusion PDEs using regulation-triggered finite-time identification

Automatica ◽  
2019 ◽  
Vol 103 ◽  
pp. 166-179 ◽  
Author(s):  
Iasson Karafyllis ◽  
Miroslav Krstic ◽  
Katerina Chrysafi
Keyword(s):  
Boundary Control ◽  
Finite Time ◽  
Reaction Diffusion ◽  
Constant Parameter ◽  
Adaptive Boundary Control

Finite-time boundary control for delay reaction–diffusion systems

2018 ◽  
Vol 329 ◽  
pp. 52-63 ◽  
Author(s):  
Kai-Ning Wu ◽  
Han-Xiao Sun ◽  
Baoqing Yang ◽  
Cheng-Chew Lim
Keyword(s):  
Boundary Control ◽  
Finite Time ◽  
Reaction Diffusion ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Time Boundary

On the blow-up of solutions of a convective reaction diffusion equation

1993 ◽  
Vol 123 (3) ◽  
pp. 433-460 ◽  
Author(s):  
J. Aguirre ◽  
M. Escobedo
Keyword(s):  
Positive Solutions ◽  
Finite Time ◽  
Blow Up ◽  
Global Solutions ◽  
Reaction Diffusion ◽  
Scalar Function ◽  
Reaction Diffusion Equation ◽  
Semilinear Parabolic Equation ◽  
The Cauchy Problem ◽  
Image Position

SynopsisWe study the blow-up of positive solutions of the Cauchy problem for the semilinear parabolic equationwhere u is a scalar function of the spatial variable x ∈ ℝN and time t > 0, a ∈ ℝV, a ≠ 0, 1 < p and 1 ≦ q. We show that: (a) if p > 1 and 1 ≦ q ≦ p, there always exist solutions which blow up in finite time; (b) if 1 < q ≦ p ≦ min {1 + 2/N, 1 + 2q/(N + 1)} or if q = 1 and 1 < p ≦ l + 2/N, then all positive solutions blow up in finite time; (c) if q > 1 and p > min {1 + 2/N, 1 + 2q/N + 1)}, then global solutions exist; (d) if q = 1 and p > 1 + 2/N, then global solutions exist.

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