Fourier truncation regularization method for simultaneous inversion in parabolic equations with convective term

This paper aims to recover the initial value and source term simultaneously in the parabolic equations with convective term from measurements at two fixed times (Formula presented.) and (Formula presented.). In particular, we analyze the ill-posedness of the inverse problem and then apply the Fourier truncated regularization method to solve the inverse problem. A theoretical analysis of the error estimation for the initial value and source term is also given. Finally, we present some numerical examples to verify the validity and feasibility of the proposed method.