An inverse problem for a heat equation with piecewise-constant thermal conductivity

N. S. Hoang, A. G. Ramm

The governing equation is $u_t=(a(x)u_x{)}_x$, $0\le x\le 1$, $t>0$, $u(x,0)=0$, $u(0,t)=0$, $a(1)u^{\prime }(1,t)=f(t)$. The extra data are $u(1,t)=g(t)$. It is assumed that $a(x)$ is a pi…