Work

Infinite Horizon Control Problems for Semilinear Parabolic Equations with Pointwise State Constraints

Year: 2026

Type: article

Abstract: We study an optimal control problem for semilinear parabolic equations with infinite horizon, pointwise state contraints and two different types of control constraints (pointwise in space and time, and pointwise in time and $$L^2$$ L 2 in space). First we prove first-order necessary conditions, then we provide a second-order sufficient condition for local optimality. The second-order condition is formulated using an extended cone that considers the infinite horizon and the control and state constraints. This condition is sufficient for strict local optimality in the $$L^2$$ L 2 -sense. Finally, we address the approximation of the infinite horizon control problem by finite horizon problems. We analyze the convergence of these approximations and provide error estimates.

Source: Applied Mathematics & Optimization

DOI: 10.1007/s00245-026-10411-5

Authors: Lorena Bociu, Eduardo Casas

Institutions: North Carolina State University, Universidad de Cantabria

Language: English

Topic: Stability and Controllability of Differential Equations

Subfield: Control and Systems Engineering

Field: Engineering

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,890

Funders: National Science Foundation, Agencia Estatal de Investigación