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

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dc.creatorHoermann, Guenther
dc.creatorOparnica, Ljubica
dc.date2006-06-02
dc.date2007-04-12
dc.date.accessioned2026-07-07T07:56:15Z
dc.date.available2026-07-07T07:56:15Z
dc.descriptionWe 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.
dc.description3 figures
dc.identifierhttps://arxiv.org/abs/math/0606058
dc.identifierhttp://arxiv.org/abs/math/0606058
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/127242
dc.subjectAnalysis of PDEs
dc.subjectFunctional Analysis
dc.subject46F10;34A36
dc.titleDistributional solution concepts for the Euler-Bernoulli beam equation with discontinuous coefficients
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