Nonhomogeneous heat equation: Identification and regularization for the inhomogeneous term

[摘要] We study the nonhomogeneous heat equation under the form u(t)- u(xx) = phi(t) f (x), where the unknown is the pair of functions (u, f). Under various assumptions about the function 0 and the final value in t = 1, i.e., g(x), we propose different regularizations on this ill-posed problem based on the Fourier transform associated with a Lebesgue measure. For phi not equivalent to 0 the solution is unique. (c) 2005 Elsevier Inc. All rights reserved.

[发布日期] 2005-12-01

[关键词] identification;regularization;error estimations