Abstract
We consider the problem of determining a pair of functions (u, f) satisfying the two-dimensional backward heat equation with a homogeneous Cauchy boundary condition, where ϕ and g are given approximately. The problem is severely ill-posed. Using an interpolation method and the truncated Fourier series, we construct a regularized solution for the source term f and provide Hölder-type error estimates in both L 2 and H 1 norms. Numerical experiments are provided.
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