Boundary Controllability for the Quasilinear Wave Equation
By P. Yao. 2006
49 citations recorded by the source corpus.
We study the boundary exact controllability for the quasilinear wave equation in high dimensions. Our main tool is the geometric analysis. We derive the existence of long time solutions near an equilibrium, prove the locally exact controllability around the equilibrium under some checkable geometrical conditions. We then establish the globally exact controllability in such a way that the state of the quasilinear wave equation moves from an equilibrium in one location to an equilibrium in another location under some geometrical conditions. The Dirichlet action and the Neumann action are studied, respectively. Our results show that exact controllability is geometrical characters of a Riemannian metric, given by the coefficients and equilibria of the quasilinear wave equation. A criterion of exact controllability is given, which based on the sectional curvature of the Riemann metric. Some examples are presented to verify the global exact controllability.
Subfields: Computational Theory and Mathematics, Control and Systems Engineering, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f3b3cab4497fa0d92cdc5f082e45ef88a51f5442
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In Computational Theory and Mathematics
In Control and Systems Engineering
In Mathematical Physics
Citations in the corpus
- Global smooth solutions for the quasilinear wave equation with boundary dissipation (2006, background): “In addition, some examples in [13] show that if ρ(2) is strictly convex on Ω also closely depends on the equilibrium w.”