Lack of complete stabilizability of some coupled ode-parabolic systems

Debayan Maity (1) , Debanjana Mitra (2) , Mythily Ramaswamy (3)

1 TIFR-CAM - Center for Applicable Mathematics [Bangalore]
2 Department of Mathematics, Indian Institute of Technology Bombay, Powai, Maharashtra 400076, India
3 ICTS-TIFR - International Centre for Theoretical Sciences [TIFR]

In this article, we consider several coupled ode-parabolic systems. These systems are known to be not null controllable at any time by localized interior controls. We show that these systems are not exponentially stabilizable with arbitrary decay rates. And, consequently, we recover the known results that they are not null controllable any time.

Domaines: Equations aux dérivées partielles [math.AP]

Debayan Maity, Debanjana Mitra, Mythily Ramaswamy. Lack of complete stabilizability of some coupled ode-parabolic systems. 2021. ⟨hal-03346170⟩