可伸展热弹性梁系统的整体吸引子
Global Attractors for an Extensible Thermoelastic Beam System
摘要：
本工作的重点是耗散系统描述的动态可扩展的热弹性梁，其中的耗散是完全由第二个方程统治的温度的演变。在自然边界条件下，证明了有界吸收集的存在性。当外力和热源都与时间无关时，相应的解半群对于所有的轴向外力都具有最优正则性的全局吸引子.当考虑转动惯量时，同样的结果也成立。在这两种情况下，吸引子上的解都是强解。
英文摘要：
This work is focused on the dissipative system describing the dynamics of an extensible thermoelastic beam, where the dissipation is entirely contributed by the second equation ruling the evolution of the temperature. Under natural boundary conditions, we prove the existence of bounded absorbing sets. When both the external body force and the heat source are time-independent, the related semigroup of solutions is shown to possess the global attractor of optimal regularity for all values of the external axial load. The same result holds true when the rotational inertia is taken into consideration. In both cases, the solutions on the attractor are strong solutions.
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