| Abstract: |
| A nonlinear partial differential control system arising in the moisture transport in concrete carbonation modelling is considered. The system consists of a diffusion equation for moisture and an ordinary differential equation accounting for the hysteresis effect appearing in the process. The control function is subject to a state-dependent and nonconvex constraint. We prove the existence of solutions to the system and establish some of its properties such as relaxation and bang-bang principle: the density in an appropriate topology of solutions and extreme solutions of the original system among those of the system with the convexified control constraint. |
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