Distributional solution concepts for the Euler-Bernoulli beam equation with discontinuous coefficients

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

We study existence and uniqueness of distributional solutions to the differential equation of the Euler-Bernoulli rod with discontinuous coefficients and right-hand side. Upon checking the validity of a solution the occurring products of singular coefficients with the distributional solution have no obvious meaning. When interpreted on the most general level of the so-called hierarchy of distributional products, it turns out that existence of a solution forces a minimum regularity to hold. Curiously, the choice of the distributional product concept is thus incompatible with the possibility of having a discontinuous displacement function as a solution. We also give conditions for unique solvability.
3 figures

Keywords

Analysis of PDEs, Functional Analysis, 46F10;34A36

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/127242

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0606058
 http://arxiv.org/abs/math/0606058

Collections

arXiv