L ∞ -error estimates for solutions of the Helmholtz equation with truncated index in a fold caustic model
Résumé
This note considers the error estimates for the solutions of high-frequency Helmholtz equations, that is, waves refracted by a surface, in the domain when the indices of refraction coincide. We derive error estimates in terms of the wave number k > 0 for truncated indexes of refraction, thereby adapting the physical meaning of the wave equations through the use of Airy functions and their derivatives.