Vegetation pattern dynamics is a pivotal research domain in ecology, which can reveal the
impact of the non-uniform distribution of vegetation on ecosystem structure and function …

We consider the initial/boundary value problem for a diffusion equation involving multiple
time-fractional derivatives on a bounded convex polyhedral domain. We analyze a space …

In this paper a review of the results on sparse controls for partial differential equations is
presented. There are two different approaches to the sparsity study of control problems. One …

A directional sparsity framework allowing for measure valued controls in the spatial direction
is proposed for parabolic optimal control problems. It allows for controls which are localized …

Optimal control problems with semilinear parabolic state equations are considered. The
objective features one out of three different terms promoting various spatio-temporal sparsity …

This work concentrates on a class of optimal control problems for semilinear parabolic
equations subject to control constraint of the form‖ u (t)‖ L 1 (Ω)≤ γ for t∈(0, T). This limits …

Optimal control problems in measure spaces governed by semilinear elliptic equations are
considered. First order optimality conditions are derived and structural properties of their …

Optimal control problems in measure spaces governed by parabolic equations with are
considered. The controls appear as spatial measure in the initial condition and as space …

It is well known that finite element solutions for elliptic PDEs with Dirac measures as source
terms converge, due to the fact that the solution is not in H^1, suboptimal in classical norms …

A precise characterization of the extremal points of sublevel sets of nonsmooth penalties
provides both detailed information about minimizers, and optimality conditions in general …