Variational data assimilation for a nonstationary heat conduction problem with nonlinear diffusion

Abstract

We consider the problem of variational assimilation of observational data with the aim to reconstruct the initial condition in a locally one-dimensional model of vertical heat exchange in the ocean, which is described by the nonstationary heat equation with a nonlinear diffusion coefficient. We investigate the solvability of the data assimilation problem, develop and justify algorithms for its numerical solution. The results of numerical experiments are given.