An optimization problem in heat conduction with minimal temperature constraint, interior heating and exterior insulation
Hui Yu
TL;DR
This paper investigates the optimal temperature distribution in heat conduction problems involving interior heating, exterior insulation, and a minimal temperature constraint, establishing existence, regularity, and boundary properties.
Contribution
It proves the existence and regularity of optimal temperature configurations and analyzes the regularity of free boundaries in such heat conduction problems.
Findings
Existence of optimal temperature configurations.
Regularity results for the temperature and free boundaries.
Analysis of the regularity of free boundaries.
Abstract
We show the existence and optimal regularity of the optimal temperature configuration in a problem in heat conduction with minimal temperature constraint, interior heating and exterior insulation. Regularity of the two free boundaries is also studied.
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Taxonomy
TopicsAdvanced Mathematical Modeling in Engineering · Nonlinear Partial Differential Equations · Advanced Numerical Methods in Computational Mathematics