Geodesic
A nonhomogeneous backward heat problem: regularization and error estimates
Electronic journal of differential equations, Tome 2008 (2008)
We consider the problem of finding the initial temperature, from the final temperature, in the nonhomogeneous heat equation

$\displaylines{ u_t-u_{xx}= f(x,t),\quad (x,t)\in (0,\pi)\times (0,T),\cr u(0,t)= u(\pi,t)= 0, \quad (x,t) \in (0,\pi)\times(0,T). }$

This problem is known as the backward heat problem and is severely ill-posed. Our goal is to present a simple and convenient regularization method, and sharp error estimates for its approximate solutions. We illustrate our results with a numerical example.
Classification : 35K05, 35K99, 47J06, 47H10
Keywords: backward heat problem, ill-posed problem, nonhomogeneous heat equation, contraction principle 
@article{EJDE_2008__2008__a73,
     author = {Dang Duc Trong and Nguyen Huy Tuan},
     title = {A nonhomogeneous backward heat problem: regularization and error estimates},
     journal = {Electronic journal of differential equations},
     year = {2008},
     volume = {2008},
     zbl = {1171.35488},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a73/}
}
TY  - JOUR
AU  - Dang Duc Trong
AU  - Nguyen Huy Tuan
TI  - A nonhomogeneous backward heat problem: regularization and error estimates
JO  - Electronic journal of differential equations
PY  - 2008
VL  - 2008
UR  - http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a73/
LA  - en
ID  - EJDE_2008__2008__a73
ER  - 
%0 Journal Article
%A Dang Duc Trong
%A Nguyen Huy Tuan
%T A nonhomogeneous backward heat problem: regularization and error estimates
%J Electronic journal of differential equations
%D 2008
%V 2008
%U http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a73/
%G en
%F EJDE_2008__2008__a73
Dang Duc Trong; Nguyen Huy Tuan. A nonhomogeneous backward heat problem: regularization and error estimates. Electronic journal of differential equations, Tome 2008 (2008). http://geodesic.mathdoc.fr/item/EJDE_2008__2008__a73/