Optimal Control of the Thermistor Problem in Three Spatial Dimensions, Part 2: Optimality Conditions
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Publication:5348127
DOI10.1137/16M1072656zbMath1386.35227arXiv1603.04305OpenAlexW3104041651MaRDI QIDQ5348127
Hannes Meinlschmidt, Joachim Rehberg, Christian Meyer
Publication date: 14 August 2017
Published in: SIAM Journal on Control and Optimization (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1603.04305
Optimality conditions for problems involving partial differential equations (49K20) PDEs of mixed type (35M10) Quasilinear parabolic equations (35K59)
Related Items (8)
Optimal Control of Quasilinear Parabolic PDEs with State-Constraints ⋮ Purely time-dependent optimal control of quasilinear parabolic PDEs with sparsity enforcing penalization ⋮ Extrapolated elliptic regularity and application to the van Roosbroeck system of semiconductor equations ⋮ Optimal control of a quasilinear parabolic equation and its time discretization ⋮ Optimal Control of the Thermistor Problem in Three Spatial Dimensions, Part 1: Existence of Optimal Solutions ⋮ Unnamed Item ⋮ Convergence of the SQP method for quasilinear parabolic optimal control problems ⋮ Interpolation theory for Sobolev functions with partially vanishing trace on irregular open sets
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Cites Work
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- Hölder-estimates for non-autonomous parabolic problems with rough data
- Coercivity for elliptic operators and positivity of solutions on Lipschitz domains
- Automated solution of differential equations by the finite element method. The FEniCS book
- Maximal parabolic regularity for divergence operators including mixed boundary conditions
- Hölder continuity and optimal control for nonsmooth elliptic problems
- Nonautonomous parabolic equations involving measures
- A \(W^{1,p}\)-estimate for solutions to mixed boundary value problems for second order elliptic differential equations
- Resolvent estimates in \(W^{-1,p}\) for second order elliptic differential operators in case of mixed boundary conditions
- Regularity and stability for the mathematical programming problem in Banach spaces
- Maximum principle for state-constrained optimal control problems governed by quasilinear elliptic equations
- Optimal control of a parabolic equation with dynamic boundary condition
- The square root problem for second-order, divergence form operators with mixed boundary conditions on \(L^p\)
- Thermo-visco-elasticity with rate-independent plasticity in isotropic materials undergoing thermal expansion
- Maximal Parabolic Regularity for Divergence Operators on Distribution Spaces
- Boundary Control of Semilinear Elliptic Equations with Pointwise State Constraints
- Optimal Control for the Thermistor Problem
- First- and Second-Order Optimality Conditions for a Class of Optimal Control Problems with Quasilinear Elliptic Equations
- Optimal Control of a Convective Boundary Condition in a Thermistor Problem
- NUMERICAL MODELING OF INDUCTION HEATING FOR TWO-DIMENSIONAL GEOMETRIES
- Second Order Sufficient Optimality Conditions for Parabolic Optimal Control Problems with Pointwise State Constraints
- A Nonlinear Conjugate Gradient Method with a Strong Global Convergence Property
- Optimal Sobolev Regularity for Linear Second-Order Divergence Elliptic Operators Occurring in Real-World Problems
- Feasible and Noninterior Path‐Following in Constrained Minimization with Low Multiplier Regularity
- Analysis of Optimal Control Problems for the Two-Dimensional Thermistor System
- Optimal Control of the Thermistor Problem in Three Spatial Dimensions, Part 1: Existence of Optimal Solutions
- Optimal control for the thermistor problem with a current limiting device
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