Boundary Controllability for the Quasilinear Wave Equation

Journal Article · Thu Apr 15 04:00:00 EDT 2010 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-009-9088-7· OSTI ID:21480271

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.

• OSTI ID: 21480271
• Journal Information: Applied Mathematics and Optimization, Journal Name: Applied Mathematics and Optimization Journal Issue: 2 Vol. 61; ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

97 MATHEMATICS AND COMPUTING
BOUNDARY-VALUE PROBLEMS
DIFFERENTIAL EQUATIONS
DIRICHLET PROBLEM
EQUATIONS
EQUILIBRIUM
EXACT SOLUTIONS
GEOMETRY
MATHEMATICAL SOLUTIONS
MATHEMATICAL SPACE
MATHEMATICS
METRICS
PARTIAL DIFFERENTIAL EQUATIONS
RIEMANN SPACE
SPACE
WAVE EQUATIONS