Reconstruction of the initial condition in parabolic equations with Log-Lipschitz coefficients

Daniele Del Santo, Martino Prizzi

Published 2024-01-08Version 1

We consider a parabolic equation whose coefficients are Log-Lipschitz continuous in $t$ and Lipschitz continuous in $x$. Combining a recent conditional stability result with a well posed variational problem, we reconstruct the initial condition of an unknown solution from a rough measurement at the final time.