Wavelet and error estimation of surface heat flux (Q1863687)

The authors discuss the determination of the heat flux \( u_x(x,t)\) for \( 0<x<1 \) from the following problem: \[ \begin{cases} u_{xx} = u_t, \quad & x \geq 0, t>0 , \\ u(x,0) = 0, \quad ,& x \geq 0, \\ u(1,t) = g(x), \quad & t \geq 0, u|_{t \to \infty}\text{ bounded.}\end{cases} \] They present a wavelet regularization method for this ill-posed problem. An error estimate and the convergence of the regularizations approximate solution at zero are obtained.