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摘要
We consider the problem of determining a pair of functions (u, f) satisfying the two-dimensional backward heat equation
u(t) - Delta u = phi(t)f(x,y), t is an element of (0, T), (x, y) is an element of (0, 1) x (0, 1), u(x, y, T) = g(x, y)
with a homogeneous Cauchy boundary condition, where phi 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 L-2 and H-1 norms. Numerical experiments are provided.
- 出版日期2010
