Abstract The Cauchy problem for the inhomogeneous Helmholtz equation with non-uniform refraction index is considered. The ill-posedness of this problem is tackled by means of the variational form of mollification. This approach is proved to be consistent, and the proposed numerical simulations are quite promising. 

/pdf/a-mollifier-approach-to-regularize-a-cauchy-problem-for-the-vr5wnhxy.pdf

A mollifier approach to regularize a Cauchy problem for the inhomogeneous Helmholtz equation

The Cauchy problem for the inhomogeneous Helmholtz equation with non-uniform refraction index is considered. The ill-posedness of this problem is tackled by means of the variational form of mollification. This approach is proved to be consistent, and the proposed numerical simulations are quite promising.

A mollifier approach to regularize a Cauchy problem for the inhomogeneous Helmholtz equation.

Partial differential equations, 1952-1953

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Partial differential equations, 1952-1953