On the invertibility of a Prandtl type operator in Sobolev spaces on a semi-line
by
Luis Castro
Department of Mathematics & Research Unit Mathematics and Applications, University of Aveiro, Portugal

Motivated by applications in elasticity theory and hydrodynamics (e.g. in aircraft wing motion), we consider an operator theoretical study for an integro-differential Prandtl type operator in the framework of Sobolev spaces. Equivalence relations between this operator and corresponding Wiener-Hopf type operators are constructed and, therefore, we are allowed to take profit of the known theory of this second kind of operators. The main results are a Fredholm characterization and invertibility properties of the operators in study, depending on the integrability and smoothness indices of the Sobolev spaces in use.

Date received: March 31, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # canw-26.