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This work deals with the optimal control of a free boundary value problem in thermoelasticity where the geometry varies with respect to time. Typical applications are glass shaping for different purposes. We derive a mathematical model for one- and two-dimensional problems. The goal of the optimization is to achieve a desired shape of the domain by controlling the temperature inputs. In dimension one, both analysis and numerics are performed. The state-constrained problem is considered and its Moreau-Yosida regularization is analyzed. The numerical observations are presented which underline the findings from the theory. The deformation of a rectangular domain is studied in two-dimensional case and the goal is to reach a predefined profile of one of the free boundaries of the domain.
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Optimal Control of Free Boundary Value Problems in Thermoelasticity, Chathuri Fernando
- Sprache
- Erscheinungsdatum
- 2018
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- Titel
- Optimal Control of Free Boundary Value Problems in Thermoelasticity
- Sprache
- Englisch
- Autor*innen
- Chathuri Fernando
- Verlag
- Dr. Hut
- Erscheinungsdatum
- 2018
- ISBN10
- 3843936749
- ISBN13
- 9783843936743
- Reihe
- Mathematik
- Kategorie
- Mathematik
- Beschreibung
- This work deals with the optimal control of a free boundary value problem in thermoelasticity where the geometry varies with respect to time. Typical applications are glass shaping for different purposes. We derive a mathematical model for one- and two-dimensional problems. The goal of the optimization is to achieve a desired shape of the domain by controlling the temperature inputs. In dimension one, both analysis and numerics are performed. The state-constrained problem is considered and its Moreau-Yosida regularization is analyzed. The numerical observations are presented which underline the findings from the theory. The deformation of a rectangular domain is studied in two-dimensional case and the goal is to reach a predefined profile of one of the free boundaries of the domain.