Holder-Type Approximation for the Spatial Source Term of a Backward Heat Equation.

We consider the problem of determining a pair of functions (u, f) satisfying the two-dimensional backward heat equation [image omitted] 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 Holder-type error estimates in both L2 and H1 norms. Numerical experiments are provided. [ABSTRACT FROM AUTHOR]