Abstract
In this Note, we prove the existence and uniqueness of the solution to the Helmholtz equation with second order absorbing boundary conditions in a rectangle. The problem is completed by appropriate corner conditions. The formal approach makes use of a regularity result for the solution of the homogeneous problem. To this aim, one has to consider explicitly the singularities of the Laplacian.
| Translated title of the contribution | Un résultat d'existence et d'unicité pour l'équation de Helmholtz avec conditions aux limites absorbantes d'ordre 2 |
|---|---|
| Original language | English |
| Pages (from-to) | 193-198 |
| Number of pages | 6 |
| Journal | Comptes Rendus de l'Academie des Sciences - Series I: Mathematics |
| Volume | 329 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - 1 Aug 1999 |