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

摘要

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.