Determine the spacial term of a two-dimensional heat source
Abstract
We consider the problem of determining a pair of functions (u,f) satisfying the heat equation ut - u =(t)f (x,y), where (x,y)∈ =(0,1)× (0,1) and the function is given. The problem is ill-posed. Under a slight condition on , we show that the solution is determined uniquely from some boundary data and the initial temperature. Using the interpolation method and the truncated Fourier series, we construct a regularized solution of the source term f from non-smooth data. The error estimate and numerical experiments are given.
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