Sep 2026· Far East Journal of Mathematical Sciences (FJMS)· Vol 143, pp. 3795-3809· 0 citations
Abstract
In this article, we study an optimal control problem associated with a nonlinear hyperbolic equation, including cubic polynomial nonlinearity and homogeneous Neumann conditions. Starting from an integral functional dependent on the initial data and the right-hand side of the equation, we establish the necessary conditions for optimality using a variational approach. The analysis is based on the differentiability of a functional and on the solution of the adjoint problem, allowing the formulation of the Hamiltonian and the first-order conditions. The results obtained apply to a wide class of controlled problems governed by nonlinear hyperbolic partial differential equations.
Parametric optimal control problems for semilinear parabolic equations are considered. Using recent Lipschitz stability results for solutions of such problems, it is shown that, under standard coercivity conditions, the solutions are Bouligand differentiable (in
L^p
L
p
, p finite) functions o...
K. Malanowski· Journal of Convex Analysis· 5 citations· ⚡1
We study a PDE-constrained optimization problem for an elliptic equation with the spectral fractional Laplacian and a linear combination of Dirac measures as the forcing term; the controls are the amplitudes of these singular sources. We prove existence and uniqueness of an optimal solution and derive first-order optim...
This paper is concerned with the solvability of a class of nonlinear variational inequalities involving pointwise unilateral constraints on the laplacian. We describe the set of the pairs (ψ,h) of the right hand sides h and the obstacles ψ for which the problem has solutions and study the structure of the set of soluti...
R. Molle, D. Passaseo· Journal of Convex Analysis· 0 citations
Using advanced concepts and techniques from convex and variational analysis (such as the notion of twice epi-differentiability), we establish, under a set of appropriate conditions (including a polyhedricity assumption), that the solution to a parameterized nonlinear variational inequality associated with a positively...
Samir Adly, L. Bourdin· Journal of Convex Analysis· 0 citations
We investigate a parametric optimal control problem governed by a time dependent parabolic equation, where the control is a spatially varying diffusion coefficient. The objective is to minimize a tracking type cost functional under box constraints on the control. We establish the well posedness of the state equation, p...
M. Dani, M. Lamnii, A. Ouahab· Gulf Journal of Mathematics· 0 citations
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