Науковий семінар кафедри математичної фізики (Архів)
Організатор:
Місце проведення: Корпус механіко-математичного факультету КНУ, 209, 14.30
Місце проведення: Корпус механіко-математичного факультету КНУ, 209, 14.30
| Дата та час | Семінар |
|---|---|
| 06, May 2008 14:30 Tuesday | A variational approach for a subclass of regular elliptic boundary value problems leading to boundary integral equation and boundary integral operators професор W.L. Wendland (Штутгартський університет, Німеччина) Резюме: For second order formally positive elliptic linear systems (in the sense of M.~Vishik), their variational formulation and the use of the fundamental solution leads to the representation of the solutions in terms of Newton and boundary potentials with the Cauchy data as boundary charges on the Lipschitz boundary. Then G{\aa}rding's inequality in the interior as well as the exterior domain leads to G{\aa}rding inequalities for the simple layer and the hypersingular boundary integral operators on the boundary which constitute the basic properties for corresponding Galerkin approximations. In case of strong coerciveness, these equations also imply contraction properties of the double layer potential operators in appropriate Sobolev spaces, which yield convergence of Carl Neumann's classical sukzessive approximation. In the form of boundary element approximation, i.e., finite elements on the boundary, the boundary integral equations can be used for the simulation of industrial applications if appropriate fast solution methods are employed. Some examples of electrical as well as elastic fields will be presented. |