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What is Ill-posedness in 1D Heat Equation Control about?

This document discusses the ill-posedness of controlling a 1D heat equation through Dirichlet boundary control. It begins by introducing the heat equation problem and noting that controlling to a desired state is not exactly possible, only approximately. The problem is ill-posed in Sobolev spaces. It then discusses previous work on controllability and establishes a variational formulation using duality to account for lack of Dirichlet data smoothness. The main part analyzes the ill-posedness through F

Author

Faris Fathudinulhaq

Language

EN