Carleman weight functions for solving ill-posed Cauchy problems for quasilinear PDEs

Abstract

This is the first publication in which a numerical method with rigorously guaranteed convergence is presented for some ill-posed Cauchy problems for semilinear PDEs of the second order. The key tool is the use of the Carleman weight functions in a Tikhonov-like functionals. The method works for elliptic, parabolic and hyperbolic semilinear equations of the second order.