热方程数据同化问题的非典型方法

Abstract

Abstract:

We consider an one dimensional heat conduction model ∂_ty-Δy=0, in (0, T)×Ω, which we would like to "predict" on a time interval (T0, T₀) but for which the initial value of the state variable is unknown. However, "measures"of the solutions are known only at one point of Ω on a time interval (0, T₀) where 0<T₀<T. The classical approach in data assimilation is to look for the initial value at time 0 and this is known to be an ill-posed problem for heat equations. In this paper, by the property of null controllability of heat equations we give a result of approximate reconstruction of the value at T₀. The approximation needs a sharp estimation of the cost of the null controllability of the heat equation.

Key words: Data assimilation, Heat equation, Null controllability, Stability

CLC Number:

93B05

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YU Hang. Data Assimilation: a Nonstandard Approach to a Heat Conduction Model[J].Acta mathematica scientia,Series A, 2011, 31(4): 857-865.

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Data Assimilation: a Nonstandard Approach to a Heat Conduction Model

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