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Optimal control problems for semilinear elliptic equations
with control constraints and pointwise state constraints are
studied. Several theoretical results are derived, which are
necessary to carry out a numerical analysis for this class of
control problems. In particular, sufficient second-order optimality
conditions, some new regularity results on optimal controls and a
sufficient condition for the uniqueness of the Lagrange multiplier
associated with the state constraints are presented.
Sufficient conditions for the stresses in the threedimensional linearized coupled thermoelastic system including viscoelasticity to be continuous and bounded are derived and optimization of heating processes described by quasicoupled or partially linearized coupled thermoelastic systems with constraints on stresses is treated. Due to the consideration of heating regimes being “as nonregular as possible” and because of the well-known lack of results concerning the classical regularity of solutions...
We consider control problems governed by semilinear
parabolic equations with pointwise state constraints and controls in an
Lp-space (p < ∞). We construct a correct relaxed problem, prove some relaxation
results, and derive necessary optimality conditions.
We consider control problems governed by semilinear parabolic equations with pointwise state constraints and controls in an -space (). We construct a correct relaxed problem, prove some relaxation results, and derive necessary optimality conditions.
In this paper we study a control problem for elliptic nonlinear monotone problems with Dirichlet boundary conditions where the control variables are the coefficients of the equation and the open set where the partial differential problem is studied.
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