An adaptive algorithm for determination of source terms in a linear parabolic problem

Abstract

Abstract This paper investigates an adaptive algorithm for identification of source terms w : = { F ( x , t ) ; p ( t ) } ${w:=\lbrace F(x,t);p(t)\rbrace }$ in the linear parabolic equation u t = u x x + F ( x , t ) $u_t= u_{xx} + F(x,t)$ and Robin boundary condition - u x ( l , t ) = ν [ u ( l , t ) - p ( t ) ] ${-u_x(l,t)= \nu [u(l,t) - p(t)]}$ from the measured final data and the measurement of the temperature in a subregion. This is based on the minimization of Tikhonov functional. We pursue the approach iteratively regularized gradient method. Results with the adaptive algorithm are presented.