Some optimal control problems of heat equations with weighted controls

Abstract

Abstract In this paper, the time and norm optimal control problems of controlled heat equations with a weight function are considered. For the time optimal problems, we study the following two cases: one is for equations with multi-domain control under null controllability, and the other is for equations under approximate null controllability. We prove the solvability, and obtain the bang-bang principle of the time optimal controls for aforementioned both cases. For the norm optimal control problems, we focus on equations with multi-time and multi-domain control, and present the solvability of these problems.

Keywords

• heat equation
• weight function
• optimal control problem
• multi-domain