Prescribed-time and output feedback stabilization of heat equation with intermediate-point heat source and boundary control

This paper addresses the problem of prescribed-time stabilization for the heat equation with an interior point heat source under output feedback. The study employs a two-step backstepping approach along with time- varying feedback techniques. A prescribed-time state observer and an observer-based boundary control law are developed. The proposed method extends the applicability of the prescribed time-stabilizing algorithm to heat equations with non-strict feedback terms. Numerical simulations validate its effectiveness.