18 citations · 26 across the 9 of their papers we have counts for
11 papers
Optimality conditions for sparse optimal control of viscous Cahn-Hilliard systems with logarithmic potential
Pierluigi Colli, Jürgen Sprekels, Fredi Tröltzsch
In this paper we study the optimal control of a parabolic initial-boundary value problem of viscous Cahn-Hilliard type with zero Neumann boundary conditions. Phase field systems of…
Second-order sufficient conditions in the sparse optimal control of a phase field tumor growth model with logarithmic potential
Jürgen Sprekels, Fredi Tröltzsch
This paper treats a distributed optimal control problem for a tumor growth model of viscous Cahn--Hilliard type. The evolution of the tumor fraction is governed by a thermodynamic…
Second-order sufficient conditions for sparse optimal control of singular Allen--Cahn systems with dynamic boundary conditions
Jürgen Sprekels, Fredi Tröltzsch
In this paper we study the optimal control of a parabolic initial-boundary value problem of Allen--Cahn type with dynamic boundary conditions. Phase field systems of this type gove…
Space-time finite element methods for the initial temperature reconstruction
Ulrich Langer, Olaf Steinbach, Fredi Tröltzsch +1
This work is devoted to the reconstruction of the initial temperature in the backward heat equation using the space-time finite element method on fully unstructured space-time simp…
Unstructured space-time finite element methods for optimal control of parabolic equations
Ulrich Langer, Olaf Steinbach, Fredi Tröltzsch +1
This work presents and analyzes space-time finite element methods on fully unstructured simplicial space-time meshes for the numerical solution of parabolic optimal control problem…
Unstructured Space-Time Finite Element Methods for Optimal Sparse Control of Parabolic Equations
Ulrich Langer, Olaf Steinbach, Fredi Tröltzsch +1
We consider a space-time finite element method on fully unstructured simplicial meshes for optimal sparse control of semilinear parabolic equations. The objective is a combination…
First and Second Order Optimality Conditions for the Control of Fokker-Planck Equations
M. Soledad Aronna, Fredi Tröltzsch
In this article we study an optimal control problem subject to the Fokker-Planck equation \[ \partial_t ρ- νΔρ- {\rm div } \big(ρB[u]\big) = 0. \] The control variable is time-…
Optimal time delays in a class of reaction-diffusion equations
Eduardo Casas, Mariano Mateos, Fredi Tröltzsch
A class of semilinear parabolic reaction diffusion equations with multiple time delays is considered. These time delays and corresponding weights are to be optimized such that the…
Measure Control of a Semilinear Parabolic Equation with a Nonlocal Time Delay
Eduardo Casas, Mariano Mateos, Fredi Tröltzsch
We study a control problem governed by a semilinear parabolic equation. The control is a measure that acts as the kernel of a possibly nonlocal time delay term and the functional i…
Control of traveling localized spots
Steffen Martens, Christopher Ryll, Jakob Löber +2
Traveling localized spots represent an important class of self-organized two-dimensional patterns in reaction-diffusion systems. We study open-loop control intended to guide a stab…
Analytical, Optimal, and Sparse Optimal Control of Traveling Wave Solutions to Reaction-Diffusion Systems
Christopher Ryll, Jakob Löber, Steffen Martens +2
This work deals with the position control of selected patterns in reaction-diffusion systems. Exemplarily, the Schlögl and FitzHugh-Nagumo model are discussed using three different…