Event
01_1
| 제출번호(No.) | 0085 |
|---|---|
| 분류(Section) | Contributed Talk |
| 분과(Session) | Applied Mathematics (AM) |
| 영문제목 (Title(Eng.)) |
Shallow arches with a strong damping term |
| 저자(Author(s)) |
Jun Hong Ha1 Korea University of Technology and Education1 |
| 초록본문(Abstract) | Building long span arch roofs and bridges has been an important practical problem that has occupied structural engineers for many years. The motion of such structures has been studied by engineers and mathematicians since at least 1930s. General mathematical models for the motion of arches and membrane like structures has been studied after 1970s, and an interesting one of them is given by the following non-local integro-differential equation \begin{equation} \label{intro:eq:emer} \begin{array}{l} \displaystyle y_{tt}+\alpha\Delta^2 y -\left(\beta+\gamma\int_\Omega|\nabla y|^2\, dx \right) \Delta y +\kappa y_t+\mu\Delta^2 y_t =f. \end{array} \end{equation} The function $y=y(x,t)$ describing the membrane's deflection is defined on $\Omega \times (0,T)$, where $\Omega\in {\mathbf R}^d$. In the one-dimensional case $d=1$, function $y(x,t)$ describes the deflection of an arch, which is positioned over the interval $\Omega=(0,l)$ of the $x$ axis. This presentation talks about a rigorous mathematical framework for the behavior of arch and membrane like structures. Our main goal is to incorporate moving point loads $f=f(x,t)$, for an example $f=Q \delta(x-ct)$. The existence and uniqueness of weak solutions of (\ref{intro:eq:emer}) are proved, and the convergence is discussed when $\mu \to 0$. The theory is applied to a car moving on a bridge. |
| 분류기호 (MSC number(s)) |
35L75 |
| 키워드(Keyword(s)) | shallow arches, damping, Cahuchy problem |
| 강연 형태 (Language of Session (Talk)) |
Korean |