Controlability of parabolic and hyperbolic partial differential equations, and of their finite difference approximations, with respect to the shape of the domain

Details Controlability of parabolic and hyperbolic partial differential equations, and of their finite difference approximations, with respect to the shape of the domain Controlability of parabolic and hyperbolic partial differential equations, and of their finite difference approximations, with respect to the shape of the domain

2007-05-29

arxiv.org/abs/0705.4221v2

Mathematics

Analysis of PDEs

33 pages

Scientific paper

In this article we study a controllability problem for parabolic and hyperbolic partial differential equations in which the control is the shape of the domain where the equation holds. Given a right-hand source term, the quantity to control is the trace of the solution into an open subdomain and at a given time. The mapping that associates this trace to the shape of the domain is non-linear. In this paper we first consider the continuous control problem and show an approximate controllability property for the linearized parabolic problem and an exact local controlability for the hyperbolic problem. Next we address the same questions in the context of a finite difference spatial semi-discretization. We prove a local controllability result for the parabolic problem, and an exact controllability for the hyperbolic one, applying the local surjectivity theorem together with a unique continuation property of the underlying adjoint discrete system.

Affiliated with

Also associated with

No associations

Rating

Controlability of parabolic and hyperbolic partial differential equations, and of their finite difference approximations, with respect to the shape of the domain 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 Controlability of parabolic and hyperbolic partial differential equations, and of their finite difference approximations, with respect to the shape of the domain, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Controlability of parabolic and hyperbolic partial differential equations, and of their finite difference approximations, with respect to the shape of the domain will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-499327