On unbounded optimal controls in coefficients for ill-posed elliptic dirichlet boundary value problems

ПРО НЕОБМЕЖЕНІ ОПТИМАЛЬНІ КЕРУВАННЯ В КОЕФІЦІЄНТАХ ДЛЯ ПОГАНО ОБУМОВЛЕНИХ ЕЛІПТИЧНИХ КРАЙОВИХ ЗАДАЧ

Thierry Horsin (1) , Peter Kogut (2)

1 M2N - Modélisation mathématique et numérique
2 DNU - Dnipropetrovsk National University

We consider an optimal control problem associated to Dirichlet boundary value problem for linear elliptic equations on a bounded domain Ω. We take the matrix-valued coecients A(x) of such system as a control in L 1 (Ω; R N × R N). One of the important features of the admissible controls is the fact that the coecient matrices A(x) are non-symmetric, unbounded on Ω, and eigenvalues of the symmetric part A sym = (A + A t)/2 may vanish in Ω.

Keywords: degenerate elliptic equations; control in coecients; weighted Sobolev spaces; variational convergence

Domains: Mathematics [math]; Mathematics [math]; Optimization and Control [math.OC]

Thierry Horsin, Peter Kogut. On unbounded optimal controls in coefficients for ill-posed elliptic dirichlet boundary value problems. Вісник Дніпропетровського університету. Серія: Моделювання, 2014, 22 (8), pp.3. ⟨10.15421/141401⟩. ⟨hal-02946721⟩