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.
Funding source: Agence Nationale de la Recherche
Award Identifier / Grant number: ANR-17-CE40-0029
Funding statement: This work is supported in part by the grant ANR-17-CE40-0029 of the French National Research Agency ANR (project MultiOnde).
Acknowledgements
The authors are grateful to N. Alibaud for interesting comments and discussions during the development of the proposed methodology. They also wish to thank T. Le Minh, for nice and fruitful exchanges.
References
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