Second-order sufficient conditions for sparse optimal control of singular Allen-Cahn systems with dynamic boundary conditions

DOI10.3934/dcdss.2023163arXiv2303.16708OpenAlexW4386626934MaRDI QIDQ6189973

Fredi Tröltzsch, Juergen Sprekels

Publication date: 5 February 2024

Published in: Discrete and Continuous Dynamical Systems. Series S (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2303.16708

zbMATH Keywords

optimal controloptimality conditionsphase field modelAllen-Cahn equationsparsitysingular potentialdynamic boundary condition

Mathematics Subject Classification ID

Optimality conditions for problems involving partial differential equations (49K20) Nonsmooth analysis (49J52) Nonlinear parabolic equations (35K55) Fréchet and Gateaux differentiability in optimization (49J50) Initial-boundary value problems for second-order parabolic equations (35K20)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• A boundary control problem for the viscous Cahn-Hilliard equation with dynamic boundary conditions
• Passing from bulk to bulk-surface evolution in the Allen-Cahn equation
• Annular and sectorial sparsity in optimal control of elliptic equations
• A note on parabolic equation with nonlinear dynamical boundary condition
• Elliptic optimal control problems with \(L^1\)-control cost and applications for the placement of control devices
• A boundary control problem for the pure Cahn-Hilliard equation with dynamic boundary conditions
• The non-isothermal Allen-Cahn equation with dynamic boundary conditions
• Compact sets in the space \(L^ p(0,T;B)\)
• Asymptotic limits and optimal control for the Cahn-Hilliard system with convection and dynamic boundary conditions
• Sparse optimal control of the Schlögl and Fitzhugh-Nagumo systems
• Sparse optimal control for fractional diffusion
• On a Cahn-Hilliard system with convection and dynamic boundary conditions
• Global solution to the Allen-Cahn equation with singular potentials and dynamic boundary conditions
• A deep quench approach to the optimal control of an Allen-Cahn equation with dynamic boundary conditions and double obstacles
• Infinite horizon sparse optimal control
• A class of quasi-linear Allen-Cahn type equations with dynamic boundary conditions
• Existence of global solutions to the Caginalp phase-field system with dynamic boundary conditions and singular potentials
• Optimal control problems with sparsity for tumor growth models involving variational inequalities
• The Allen-Cahn equation with dynamic boundary conditions and mass constraints
• Optimal Control of an Allen--Cahn Equation with Singular Potentials and Dynamic Boundary Condition
• Second Order Analysis for Optimal Control Problems: Improving Results Expected From Abstract Theory
• Directional Sparsity in Optimal Control of Partial Differential Equations
• Optimal Boundary Control of a Viscous Cahn--Hilliard System with Dynamic Boundary Condition and Double Obstacle Potentials
• Distributed and boundary optimal control of the Allen–Cahn equation with regular potential and dynamic boundary conditions
• Analysis of Spatio-Temporally Sparse Optimal Control Problems of Semilinear Parabolic Equations
• Convergence to steady states of solutions of the Cahn–Hilliard and Caginalp equations with dynamic boundary conditions
• Optimal Velocity Control of a Viscous Cahn--Hilliard System with Convection and Dynamic Boundary Conditions
• Optimal velocity control of a convective Cahn-Hilliard system with double obstacles and dynamic boundary conditions: a `deep quench' approach
• Optimal Control of the Two-Dimensional Evolutionary Navier--Stokes Equations with Measure Valued Controls
• Sparse optimal control of a phase field system with singular potentials arising in the modeling of tumor growth
• Boundary control problem and optimality conditions for the Cahn–Hilliard equation with dynamic boundary conditions
• Sparse and switching infinite horizon optimal controls with mixed-norm penalizations
• Finite element methods for surface PDEs
• Convergence to equilibrium for the semilinear parabolic equation with dynamical boundary condition
• Second Order and Stability Analysis for Optimal Sparse Control of the FitzHugh--Nagumo Equation
• Second-order analysis of a boundary control problem for the viscous Cahn--Hilliard equation with dynamic boundary condition
• Sparse Optimal Control of a Phase Field Tumor Model with Mechanical Effects
• An adaptive finite element method for the sparse optimal control of fractional diffusion

This page was built for publication: Second-order sufficient conditions for sparse optimal control of singular Allen-Cahn systems with dynamic boundary conditions