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On a three dimansional Cauchy problem for inhomogeneous Helmholtz equation associated with perturbed wave number


Quan Pham Hoang, Triet Le Minh*, Phong Luu Hong

Source title: 
Journal of Computational and Applied Mathematics, 335: 86-98, 2018 (ISI)
Academic year of acceptance: 

In recent years, the Cauchy problem for inhomogeneous Helmholtz equation (CPHE) is often considered as the wave number k is a constant number. At present, we investigate a three dimensional CPHE with inhomogeneous Cauchy conditions given at z=0 while wave number k is perturbed. The problem is well-known to be ill-posed in the sense of Hadamard. Therefore, we regularize the problem by applying the truncation method and possess error estimate between the exact solution and the regularized solution. A numerical experiment is given for the purpose of illustrating our method.