论文信息 - On Optimal Regularization Methods for the Backward Heat Equation

On Optimal Regularization Methods for the Backward Heat Equation

In this paper we consider different regularization methods for solving the heat equation u + Au = 0 (0 < i < T) backward in time, where A : H -, H is a linear (unbounded) operator in a Hubert space H with norm and z 6 are the available (noisy) data for u(T) with 11 z6 u(T)ii < 5. Assuming 11 u ( 0 )11 < E we consider different regularized solutions q(t) for u(t) and discuss the question how to choose the regularization parameter = cs(5,E,t) in order to obtain optimal estimates sup q(t) u(t)11 < E'+'&+ where the supremum is taken over z6 E H, ll u (0 )11 < E and 11 z6 u(T)II < 5.

Ulrich Tautenhahn | U. Tautenhahn | T. Schröter | T. Schröter

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