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Energy method for exponential stability of coupled one-dimensional hyperbolic PDE-ODE systems

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  • 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.

    Mathematics Subject Classification: Primary: 35L50, 47D03; Secondary: 93D20.


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  • Figure 1.  An elastic tube connected to two rigid tanks

    Figure 2.  A waveguide terminated by oscillators

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