A convergent numerical method to recover the initial condition of nonlinear parabolic equations from lateral Cauchy data

摘要: We propose a new numerical method for the solution of problem reconstruction initial condition quasilinear parabolic equation from measurements both Dirichlet and Neumann data on boundary bounded domain. Although this is highly nonlinear, we do not require an guess true solution. The key in our derivation value system coupled elliptic equations whose vector function spatially dependent Fourier coefficients to governing equation. solve by iterative method. global convergence rigorously established using Carleman estimate. Numerical examples are presented.