M 511

We consider a weighted discrete graph over , i.e. is a countable discrete set, is a function on which induces a measure and is an edge weight. Then the corresponding Laplacian is a non-negative self-adjoint operator. We investigate whether (weak) observability estimates for the corresponding heat equation exist, i.e. we study if, for given final time and a subset of , the norm of the solution of the heat equation at time can be bounded by the portions of the solution on up to time and the norm of the initial condition. We will also comment on the impact of such estimates w.r.t. controllability. This is joint work with Peter Stollmann (Chemnitz) and Martin Tautenhahn (Leipzig).

Prof. Dr. Christian Seifert

TU Hamburg