The Quasi-Reversibility Regularization for Source Inversion of a Linear Kuramoto-Sivashinsky Equation

Abstract

The source inversion problem for the linear Kuramoto-Sivashinsky equation is studied. To address the ill-posedness of the source term inversion, a quasi-reversibility regularization method is used for the stable reconstruction of the source term. In the case of noisy measurement data, the convergence (error estimate) of regularized solutions with respect to noise level is analyzed under a priori choice of the regularization parameter. Subsequently, a modified Morozov discrepancy principle is proposed to select regularization parameters for the a posteriori principle. The convergence (error estimate) of regularized solutions is established under this a posteriori principle. Numerical examples are provided to verify the effectiveness of the proposed quasi-reversibility regularization method.