Stabilizability of coupled wave equations in parallel under various boundary conditions

Boundary controllability for the quasi-linear wave equations coupled in parallel

“…Stabilization and controllability for systems coupled by linear wave equations in parallel can be found in papers [19,15,20] and [18]. Such systems of the quasi-linear case have not been considered.…”

“…Controllability for coupled linear wave equations has been investigated by many authors, we refer the readers to [15][16][17][18][19][20], etc. There are few results in higher dimensions for nonlinear cases.…”

Exact boundary controllability of coupled hyperbolic equations

“…These models also arise in a very important applied area-wave propagation in porous media (Boit, 1962;Holger et al, 2010). Stabilizability of coupled wave equations and its applications are discussed by Najafi et al (1997) and Najafi (2001).…”

The exponential decay rate of generic tree of 1-d wave equations with boundary feedback controls

“…The estimate problem of the decay rate of the system appears not only in the 1-d wave networks, but also in the other networks, for instance, the first hyperbolic systems, [16,10,9,8] for 1-d linear hyperbolic systems, [43] for thermo-elastic networks, [21] for gas networks and others [6,35]. Based on the reasons above, in this paper, we concentrate our attention on the estimate problem of the 1-d wave networks.…”