论文标题
弦/梁结构的第二声音热弹性稳定性
Second sound thermoelastic stability of a string/beam structure
论文作者
论文摘要
在本文中，我们研究了特殊的弦乐/梁结构中的一维热弹性传输问题：两个组件在接口处耦合（确定为$ 0 $）。绳子或横梁是被假定的热弹性，热通量是由卡塔内诺定律而不是通常的傅立叶定律给出的。我们证明，如果字符串是热弹性的，则整个系统的能量衰减是指数级的。当只有光束是热弹性的时，我们就会证明耦合串/梁的能量是多个身份衰减的零，以$ \ frac {1} {1} {t} $，并且衰减速率最多可以是多数层稳定的阶$ \ frac {1}}} {t^2} $。
In this paper we study the one dimensional thermoelastic transmission problem in a special string/beam structure: the two components are coupled at an interface (identified to $0$). Either the string or the beam is supposed thermoelastic, the heat flux is given by the Cattaneo's law instead of the usual Fourier's law. We prove that the the energy decay of the whole system is exponential if the string is thermoelastic. When only the beam is thermoelastic, we prove that the energy of the coupling string/beam decays polynomially to zero as $\frac{1}{t}$ and the decay rate can be, at most, polynomially stable of order $\frac{1}{t^2}$.
