具有非线性热源项的耦合杆系统

主要以经典的算子半群理论为依据,研究了一类具有非线性热效应的耦合杆系统的长时间行为.首先在齐次边界条件和初始条件下,证明了系统解的存在唯一性;其次通过渐近先验估计,证明了系统有界吸收集的存在性;最后利用算子半群的分解技巧,得到了系统全局吸引子的存在性.

The Coupled Rod System with Nonlinear Heat Source Term

In this paper,we investigate the longtime behavior of the coupled rod system with thermal effect by the classic theory of operator semigroup.Firstly,under homogeneous boundary conditions and initial conditions,the existence and uniqueness of solutions are proved;Secondly,by asymptotic a priori estimate method,the existences of the bound-ary absorbing set is obtained;Lastly,by the suitable decomposition of the semigroup,the existence of the global attractor for the coupled rod system is also given.