Global smooth solutions for the quasilinear wave equation with boundary dissipation
By P. Yao. Cybersecurity and Cyberforensics Conference, 2006
56 citations recorded by the source corpus.
We consider the existence of global solutions of the quasilinear wave equation with a boundary dissipation structure of an input-output in the higher-dimensional case when initial data and boundary inputs are near a given equilibrium of the system. Our main tool is the geometrical analysis. The main interest is to study the effect of the boundary dissipation structure on solutions of the quasilinear system. We show that the existence of global solutions depends not only on this dissipation structure but also on a Riemannian metric, given by the coefficients and the equilibrium of the system. Some geometrical conditions on this Riemannian metric are presented to guarantee the existence of global solutions. In particular, we prove that the norm of the state of the system decays exponentially if the input stops after a finite time, which implies the exponential stabilization of the system by boundary feedback.
Subfields: Applied Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/121ad839216fb94c689d6bc8ccc5cefbfa5e9d3e
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In Control and Systems Engineering
In Mathematical Physics
Citations in the corpus
- Boundary Controllability for the Quasilinear Wave Equation (2006, methodology): “The problem of stabilization is studied by [15, 19, 32, 41 ], and [43].”
- Energy decay for the Cauchy problem of the linear wave equation of variable coefficients with dissipation (2009, methodology): “1 was introduced by Yao [32] for the controllability of the wave equation with variable coefficients, which is also a useful condition for the controllability and the stabilization of the quasilinear wave equation (see [35–37]).”