TY  - JOUR
U1  - Wissenschaftlicher Artikel
A1  - Honegger, Reinhard
A1  - Lauxmann, Michael
A1  - Priwitzer, Barbara
T1  - On wave-like differential equations in general Hilbert space with application to Euler–Bernoulli bending vibrations of a beam
JF  - Partial differential equations in applied mathematics
N2  - Wave-like differential equations occur in many engineering applications. Here the engineering setup is embedded into the framework of functional analysis of modern mathematical physics. After an overview, the –Hilbert space approach to free Euler–Bernoulli bending vibrations of a beam in one spatial dimension is investigated. We analyze in detail the corresponding positive, selfadjoint differential operators of 4-th order associated to the boundary conditions in statics. A comparison with free string wave swinging is outlined.
KW  - positive selfadjoint differential operators of 4-th order
KW  - Friedrichs extension
KW  - wave-like differential equations in Hilbert space
KW  - Euler–Bernoulli (partial) differential equation
KW  - boundary conditions
KW  - Sobolev spaces
Y1  - 2024
UN  - https://nbn-resolving.org/urn:nbn:de:bsz:rt2-opus4-48448
SN  - 2666-8181
SS  - 2666-8181
U6  - https://doi.org/10.1016/j.padiff.2024.100617
DO  - https://doi.org/10.1016/j.padiff.2024.100617
VL  - 9
SP  - 1
EP  - 10
S1  - 10
PB  - Elsevier
CY  - Amsterdam
ER  -