2014/08/08 by Nguyen, Huy Tuan, Vo Anh Khoa, Khoa, Vo Anh +4
Computer Science · Engineering · Mathematics · #35K05 #35K99 #47H10 #47J06 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Microwave Imaging and Scattering Analysis #Numerical Analysis (math.NA) #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.1408.1932
openalex publication_date 2014/08/08 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28
In this paper, we rigorously investigate the truncation method for the Cauchy problem of Helmholtz equations which is widely used to model propagation phenomena in physical applications. The method is a well-known approach to the regularization of several types of ill-posed problems, including the model postulated by Regi' nska and Regi' nski \citeRR06. Under certain specific assumptions, we examine the ill-posedness of the non-homogeneous problem by exploring the representation of solutions based on Fourier mode. Then the so-called regularized solution is established with respect to a frequency bounded by an appropriate regularization parameter. Furthermore, we provide a short analysis of the nonlinear forcing term. The main results show the stability as well as the strong convergence confirmed by the error estimates in L2-norm of such regularized solutions. Besides, the regularization parameters are formulated properly. Finally, some illustrative examples are provided to corroborate our qualitative analysis.