A Non Linear Optimal Control Problem Related to a Road De-icing Device: Analysis and Numerical Experiments

In order to design a road de-icing device by heating, we consider in a two dimensional setting the optimal control of an advection–diffusion equation with a nonlinear boundary condition of the Stefan-Boltzmann type. The problem models the heating of a road during a winter period to keep positive its...

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Vydané v:Applied mathematics & optimization Ročník 91; číslo 3; s. 63
Hlavní autori: Bernardin, Frédéric, Lemoine, Jérôme, Münch, Arnaud
Médium: Journal Article
Jazyk:English
Vydavateľské údaje: New York Springer US 01.06.2025
Springer Nature B.V
Predmet:
Advection-diffusion equation
Algorithms
Applied mathematics
Asphalt pavements
Boundary conditions
Calculus of Variations and Optimal Control; Optimization
Control
Deicing
Energy
Heat transfer
Heating
Hydraulics
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Nonlinear control
Numerical and Computational Physics
Optimal control
Optimization
Partial differential equations
Roads & highways
Simulation
Systems Theory
Temperature
Theoretical
65C20
Energy
49J20
Optimal control
Unilateral constraint
Road heating
Non linear advection–diffusion equation
De-icing
ISSN:0095-4616, 1432-0606
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Popis
Shrnutí:In order to design a road de-icing device by heating, we consider in a two dimensional setting the optimal control of an advection–diffusion equation with a nonlinear boundary condition of the Stefan-Boltzmann type. The problem models the heating of a road during a winter period to keep positive its surface temperature above a given threshold. The heating device is performed through the circulation of a coolant in a porous layer of the road. We prove the well-posedeness of the nonlinear optimal control problem, subject to unilateral constraints on the control and the state, set up a gradient based algorithm then discuss some numerical results associated with real data obtained from experimental measurements. The study, initially developed in a one dimensional simpler setting in [ 1 ], aims to quantify the minimal energy to be provided to keep the road surface without frost or snow.
Bibliografia:ObjectType-Article-1
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content type line 14
ISSN:0095-4616
1432-0606
DOI:10.1007/s00245-025-10261-7