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

Pierre Maréchal (1) , Walter Cedric Simo Tao Lee (1) , Faouzi Triki (2)

1 IMT - Institut de Mathématiques de Toulouse UMR5219
2 EDP - Equations aux Dérivées Partielles

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.

Domaines: Equations aux dérivées partielles [math.AP]

Pierre Maréchal, Walter Cedric Simo Tao Lee, Faouzi Triki. A mollifier approach to regularize a Cauchy problem for the inhomogeneous Helmholtz equation. 2022. ⟨hal-03606718⟩