Open AccessEnergy method for exponential stability of coupled one-dimensional hyperbolic PDE-ODE systems
Author(s) -
Gervy Marie Angeles,
Gilbert Peralta
Publication year - 2022
Publication title -
evolution equations and control theory
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.665
H-Index - 19
eISSN - 2163-2480
pISSN - 2163-2472
DOI - 10.3934/eect.2020108
Subject(s) - mathematics , semigroup , ode , partial differential equation , hyperbolic partial differential equation , bounded function , a priori and a posteriori , mathematical analysis , exponential stability , ordinary differential equation , dissipation , exponential function , stability (learning theory) , space (punctuation) , differential equation , physics , nonlinear system , computer science , thermodynamics , philosophy , epistemology , quantum mechanics , machine learning , operating system
We consider a hyperbolic system of partial differential equations on a bounded interval coupled with ordinary differential equations on both ends. The evolution is governed by linear balance laws, which we treat with semigroup and time-space methods. Our goal is to establish the exponential stability in the natural state space by utilizing the stability with respect to the first-order energy of the system. Derivation of a priori estimates plays a crucial role in obtaining energy and dissipation functionals. The theory is then applied to specific physical models.