Generic finiteness in solving optimal control problems
Global existence for a Riccati equation arising in a boundary control problem for distributed parameters
Si prova resistenza globale della soluzione di una equazione di Riccati collegata alla sintesi di un problema di controllo ottimale. Il problema considerato rappresenta la versione astratta di alcuni problemi governati da equazioni paraboliche con il controllo sulla frontiera.
Global minimizing domains for the first eigenvalue of an elliptic operator with non-constant coefficients.
Gradient estimation of a -harmonic map.
Gradient flow for the one-dimensional Mumford-Shah functional
Grwoth conditions and regularity, a counterexample.
Hamilton-Jacobi equations for control problems of parabolic equations
We study Hamilton-Jacobi equations related to the boundary (or internal) control of semilinear parabolic equations, including the case of a control acting in a nonlinear boundary condition, or the case of a nonlinearity of Burgers' type in 2D. To deal with a control acting in a boundary condition a fractional power – where (A,D(A)) is an unbounded operator in a Hilbert space X – is contained in the Hamiltonian functional appearing in the Hamilton-Jacobi equation. This situation has already...
Homogenization of constrained optimal control problems for one-dimensional elliptic equations on periodic graphs
We are concerned with the asymptotic analysis of optimal control problems for -D partial differential equations defined on a periodic planar graph, as the period of the graph tends to zero. We focus on optimal control problems for elliptic equations with distributed and boundary controls. Using approaches of the theory of homogenization we show that the original problem on the periodic graph tends to a standard linear quadratic optimal control problem for a two-dimensional homogenized system, and...
Homogenization of constrained optimal control problems for one-dimensional elliptic equations on periodic graphs
We are concerned with the asymptotic analysis of optimal control problems for 1-D partial differential equations defined on a periodic planar graph, as the period of the graph tends to zero. We focus on optimal control problems for elliptic equations with distributed and boundary controls. Using approaches of the theory of homogenization we show that the original problem on the periodic graph tends to a standard linear quadratic optimal control problem for a two-dimensional homogenized system,...
Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1
We consider quasilinear optimal control problems involving a thick two-level junction Ωε which consists of the junction body Ω0 and a large number of thin cylinders with the cross-section of order 𝒪(ε2). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary conditions depend on parameters ε, α, β and the...
Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1∗
We consider quasilinear optimal control problems involving a thick two-level junction Ωε which consists of the junction body Ω0 and a large number of thin cylinders with the cross-section of order 𝒪(ε2). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary...
Homogenization of quasilinear optimal control problems involving a thick multilevel junction of type 3 : 2 : 1∗
We consider quasilinear optimal control problems involving a thick two-level junction Ωε which consists of the junction body Ω0 and a large number of thin cylinders with the cross-section of order 𝒪(ε2). The thin cylinders are divided into two levels depending on the geometrical characteristics, the quasilinear boundary conditions and controls given on their lateral surfaces and bases respectively. In addition, the quasilinear boundary...
Homogenization with uncertain input parameters
We homogenize a class of nonlinear differential equations set in highly heterogeneous media. Contrary to the usual approach, the coefficients in the equation characterizing the material properties are supposed to be uncertain functions from a given set of admissible data. The problem with uncertainties is treated by means of the worst scenario method, when we look for a solution which is critical in some sense.
Hyperbolic systems of partial differential inclusions
Identification of critical curves. II. Discretization and numerical realization
We consider the finite element approximation of the identification problem, where one wishes to identify a curve along which a given solution of the boundary value problem possesses some specific property. We prove the convergence of FE-approximation and give some results of numerical tests.
Inequalities of Korn's type, uniform with respect to a class of domains
Inequalities of Korn's type involve a positive constant, which depends on the domain, in general. A question arises, whether the constants possess a positive infimum, if a class of bounded two-dimensional domains with Lipschitz boundary is considered. The proof of a positive answer to this question is shown for several types of boundary conditions and for two classes of domains.
Integral characterization of functionals defined on spaces of functions
Integral Formulae Associated with the Euler-Lagrange Operators of Multiple Integral Problems in the Calculus of Variations. (Short Communication).
Integral Formulae Associated with the Euler-Lagrange Operators of Multiple Integral Problems in the Calculus of Variations.
Inverse problem of the classical calculus of variations