Optimal Control of a Parabolic Equation with Dynamic Boundary Condition

Journal Article · Fri Feb 15 00:00:00 EST 2013 · Applied Mathematics and Optimization

DOI:https://doi.org/10.1007/S00245-012-9178-9· OSTI ID:22156533

Hoemberg, D., E-mail: [e-mail]; Krumbiegel, K., E-mail: [e-mail] ^[1]; Rehberg, J., E-mail: [e-mail] ^[2]

---

1. Weierstrass Institute for Applied Mathematics and Stochastics, Nonlinear Optimization and Inverse Problems (Germany)
2. Weierstrass Institute for Applied Mathematics and Stochastics, Partial Differential Equations (Germany)

We investigate a control problem for the heat equation. The goal is to find an optimal heat transfer coefficient in the dynamic boundary condition such that a desired temperature distribution at the boundary is adhered. To this end we consider a function space setting in which the heat flux across the boundary is forced to be an L{sup p} function with respect to the surface measure, which in turn implies higher regularity for the time derivative of temperature. We show that the corresponding elliptic operator generates a strongly continuous semigroup of contractions and apply the concept of maximal parabolic regularity. This allows to show the existence of an optimal control and the derivation of necessary and sufficient optimality conditions.

• OSTI ID: 22156533
• Journal Information: Applied Mathematics and Optimization, Vol. 67, Issue 1; Other Information: Copyright (c) 2013 Springer Science+Business Media New York; Article Copyright (c) 2012 Springer Science+Business Media, LLC; Country of input: International Atomic Energy Agency (IAEA); ISSN 0095-4616
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
97 MATHEMATICAL METHODS AND COMPUTING
BOUNDARY CONDITIONS
EQUATIONS
HEAT FLUX
HEAT TRANSFER
MATHEMATICAL SPACE
MEASURE THEORY
OPTIMAL CONTROL
PARABOLAS
TEMPERATURE DISTRIBUTION