Hölder-type approximation for the spatial source term of a backward heat equation
نویسندگان
چکیده
We consider the problem of determining a pair of functions (u, f) satisfying the two-dimensional backward heat equation ut −∆u = φ(t)f(x, y), t ∈ (0, T ), (x, y) ∈ (0, 1)× (0, 1), u(x, y, T ) = g(x, y) 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 L2 and H1 norms. Numerical experiments are provided. MSC 2000: 35K05, 42A16, 65D05, 65N21.
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