Open AccessOn nonlocal boundary value problem for the equation of motion of a homogeneous elastic beam with pinned-pinned ends
Author(s) -
Taras Goy,
M. P. Negrych,
I. Ya. Savka
Publication year - 2018
Publication title -
karpatsʹkì matematičnì publìkacìï
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.63
H-Index - 4
eISSN - 2313-0210
pISSN - 2075-9827
DOI - 10.15330/cmp.10.1.105-113
Subject(s) - mathematics , sobolev space , domain (mathematical analysis) , lebesgue measure , homogeneous , measure (data warehouse) , boundary value problem , boundary (topology) , mathematical analysis , combinatorics , motion (physics) , space (punctuation) , mathematical physics , lebesgue integration , physics , classical mechanics , database , computer science , linguistics , philosophy
In the current paper, in the domain $D=\{(t,x): t\in(0,T), x\in(0,L)\}$ we investigate the boundary value problem for the equation of motion of a homogeneous elastic beam $$ u_{tt}(t,x)+a^{2}u_{xxxx}(t,x)+b u_{xx}(t,x)+c u(t,x)=0, $$ where $a,b,c \in \mathbb{R}$, $b^2 2$, then for almost all (with respect to Lebesgue measure in $\mathbb{R}$) numbers $a$ exists a unique solution $u\in\mathbf{C}^{\,2}([0,T];\mathbf{H}_{q})$ of the problem considered.