Lothar Jentsch; David Natroshvili : Non-local approach in mathematical problems of fluid-structure interaction

Author(s) :

Lothar Jentsch; David Natroshvili

Title :

Non-local approach in mathematical problems of fluid-structure interaction

Electronic source :

[gzipped dvi-file] 49 kB
[gzipped ps-file] 105 kB

Preprint series

Technische Universität Chemnitz, Fakultät für Mathematik (Germany). Preprint 98-1, 1998

Mathematics Subject Classification :

31A10 [ Integral representations of harmonic functions (two-dimensional) ]

35J05 [ Laplace equation, etc. ]

35J55 [ Systems of elliptic equations, boundary value problems ]

73B40 [ Anisotropic materials ]

Abstract :

Three-dimensional mathematical problems of interaction between elastic and scalar oscillation fields are investigated. An elastic field_is to be defined in a bounded inhomogeneous anisotropic body occupying the domain $\overline{\Omega_1} \cup \bbR^3$ while_a physical (acoustic) scalar field is to be defined in the exterior domain $\overline{\Omega_2} = \bbR^3\\ \Omega_1$ which is filled up also by an anisotropic (fluid) medium. These two fields satisfy the governing equations of steady state oscillations in the corresponding domains together with special kinematic and dynamic transmission conditions on the interface $\delta\Omega_1$. The problems are studied by the so-called non-local approach, which is the coupling of the boundary integral equation method (in the unbounded domain) and the functional-variational method (in the bounded domain). The uniqueness and existence theorems are proved and the regularity of solutions are established with the help of the corresponding Steklov-Poincare type operators and on the basis of the Garding inequality and the Lax-Milgram theorem. In particular, it is shown that the physical fluid-solid acoustic interaction problem is solvable for arbitrary values of the frequency parameter.

Keywords :

fluid-structure interaction, boundary integral method, variational method

Language :

english

Publication time :

1/1998

Notes :

This research was supported by the Deutsche Forschungsgemeinschaft (DFG) under grant number 436 GEO 17/2/97.