Hello all,

Sorry for the late notice, but we will have a CAM Seminar tomorrow

Wednesday, September 12, 3:35-4:35pm @ Ayres 113

Speaker: Abner J. Salgado

Title:
A space-time fractional optimal control problem: analysis and
discretization

Abstract:
We study a linear-quadratic optimal control problem involving a
parabolic equation with fractional diffusion and Caputo fractional time
derivative of orders $s \in (0,1)$ and $\gamma \in (0,1]$,
respectively. The spatial fractional diffusion is realized as the
Dirichlet-to-Neumann map for a nonuniformly elliptic operator. Thus, we
consider an equivalent formulation with a quasi-stationary elliptic
problem with a dynamic boundary condition as state equation. The rapid
decay of the solution to this problem suggests a truncation that is
suitable for numerical approximation. We consider a fully discrete
scheme: piecewise constant functions for the control and, for the
state, first-degree tensor product finite elements in space and a
finite difference discretization in time. We show convergence of this
scheme and, under additional data regularity, derive a priori error
estimates for the case $s \in (0,1)$ and $\gamma = 1$
-- 
Abner J. Salgado
Department of Mathematics, University of Tennessee
Knoxville, TN 37996 USA
Tel: +1 (865) 974-4314
http://www.math.utk.edu/~abnersg