@article{07278d10a2bf11df928f000ea68e967b,
title = "An approximate solution for nonlinear backward parabolic equations",
abstract = "We consider the backward parabolic equation{(ut + A u = f (t, u (t)), 0 < t < T,; u (T) = g,) where A is a positive unbounded operator and f is a nonlinear function satisfying a Lipschitz condition, with an approximate datum g. The problem is severely ill-posed. Using the truncation method we propose a regularized solution which is the solution of a system of differential equations in finite dimensional subspaces. According to some a priori assumptions on the regularity of the exact solution we obtain several explicit error estimates including an error estimate of H{\"o}lder type for all t ∈ [0, T]. An example on heat equations and numerical experiments are given.",
author = "Phan, {Thanh Nam}",
year = "2010",
month = jul,
day = "15",
language = "English",
volume = "367",
pages = "337--349",
journal = "Journal of Mathematical Analysis and Applications",
issn = "0022-247X",
publisher = "Academic Press",
number = "2",
}