scholarly journals Pointwise bounds for linear reaction-diffusion systems and an extension to nonlinear problems

1988 ◽  
Vol 135 (1) ◽  
pp. 88-111 ◽  
Author(s):  
Michael Plum
Keyword(s):  
Reaction Diffusion ◽  
Nonlinear Problems ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Linear Reaction

scholarly journals State-constrained controllability of linear reaction-diffusion systems

2021 ◽  
Author(s):  
Pierre Lissy ◽  
Clément Moreau
Keyword(s):  
Parabolic Equations ◽  
Reaction Diffusion ◽  
Coupled System ◽  
The State ◽  
Staircase Method ◽  
Reaction Diffusion Systems ◽  
Diffusion Systems ◽  
Linear Parabolic Equations ◽  
Linear Reaction ◽  
Constrained Controllability

We study the controllability of a coupled system of linear parabolic equations, with nonnegativity constraint on the state. We establish two results of controllability to trajectories in large time: one for diagonal diffusion matrices with an “approximate” nonnegativity constraint, and a another stronger one, with “exact” nonnegativity constraint, when all the diffusion coefficients are equal. The proofs are based on a “staircase” method. Finally, we show that state-constrained controllability admits a positive minimal time, even with weaker unilateral constraint on the state.

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