2 CANONICAL WEDGE PROBLEMS FOR THE HELMHOLTZ-EQUATION

Citation
E. Meister et F. Penzel, 2 CANONICAL WEDGE PROBLEMS FOR THE HELMHOLTZ-EQUATION, Mathematical methods in the applied sciences, 17(11), 1994, pp. 877-899
Citations number
18
Categorie Soggetti
Mathematical Method, Physical Science",Mathematics
ISSN journal
01704214
Volume
17
Issue
11
Year of publication
1994
Pages
877 - 899
Database
ISI
SICI code
0170-4214(1994)17:11<877:2CWPFT>2.0.ZU;2-1
Abstract
Boundary-transmission problems for two-dimensional Helmholtz equations in a quadrant and its complement, respectively, are considered in a S obolev space setting. The first problem of a quadrant with Dirichlet c ondition on one face and transmission condition on the other is solved in closed form for the case where all the quadrants are occupied by t he same medium. Unique solvability can also be shown in the case of tw o different media up to exceptional cases of wave numbers, while the F redholm property holds in general. In the second problem, transmission conditions are prescribed on both faces. Similar results are obtained in the one-medium case, but the two-media case turns out to be more c omplicated and the equivalent system of boundary pseudodifferential eq uations cannot be completely analysed by this reasoning.