The Dirichlet Problem on Wave Propagation in a 2-D Exterior Cracked Domain with Compatibility Conditions at the Tips of the Cracks
Abstract
The Dirichlet problem for the 2-D Helmholtz equation in an exterior domain with cracks is studied. The compatibility conditions at the tips of the cracks are assumed. The existence of a unique classical solution is proved by potential theory. The integral representation for a solution is obtained. The problem is reduced to the Fredholm equation of the second kind and of index zero, which is uniquely solvable.
- Publication:
-
1st International Conference on Applications of Mathematics in Technical and Natural Sciences
- Pub Date:
- October 2009
- DOI:
- 10.1063/1.3265338
- Bibcode:
- 2009AIPC.1186..271K
- Keywords:
-
- cracks;
- boundary-value problems;
- integral equations;
- functional analysis;
- 62.20.mt;
- 02.60.Lj;
- 02.30.Rz;
- 02.30.Sa;
- Cracks;
- Ordinary and partial differential equations;
- boundary value problems;
- Integral equations;
- Functional analysis