On nonlinear inverse problems of dehydratation of gypsum plasterboards exposed to fire via the heat conduction problem with radiation boundary conditions
Résumé
The paper investigates boundary optimal controls and parameter estimates to the well-posedness nonlin- ear model of dehydratation of gypsum plasterboard exposed to fire. We develop the general formulations for the boundary control for initial-boundary value problem for nonlinear partial differential equations modeling the heat transfer during a fire exposure and derive necessary optimality conditions, including the adjoint equation, for the optimal set of parameters minimizing objective functions J. Numerical simulations il- lustrate several numerical optimization methods and several examples and realistic cases, in which several interesting phenomena are observed. A large amount of computational effort is required to solve the coupled state equation and the adjoint equation (which is backwards in time), and the algebraic gradient equation (which implements the coupling between the adjoint and control variables). The state and adjoint equations are solved using the finite element method.
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