Boundary controllability for the quasilinear wave equation

Details Boundary controllability for the quasilinear wave equation Boundary controllability for the quasilinear wave equation

2006-03-13

arxiv.org/abs/math/0603280v1

Mathematics

Analysis of PDEs

47pages

Scientific paper

We study the boundary exact controllability for the quasilinear wave equation in the higher-dimensional case. 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 condition. 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.

Affiliated with

Also associated with

No associations

Rating

Boundary controllability for the quasilinear wave equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Boundary controllability for the quasilinear wave equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Boundary controllability for the quasilinear wave equation will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-69565