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

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

2006-06-02

arxiv.org/abs/math/0606058v4

Mathematics

Analysis of PDEs

3 figures

Scientific paper

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.

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