Fourier regularization of an one dimensional non-standard inverse heat conduction problem

The following non-standard inverse heat conduction problem arises in various application fields u t+u x=u xx, u(1,t)=g(t), u(x,0)=0, 0≤x∞,0t∞, 0≤t∞, x≥0. This problem is seriously ill-posed and it seems impossible to compute numerically the solution when it does not depend continuously on the data.In this paper the stability of this problem is recovered by a Fourier regularization method and the e…