摘要
In this paper, we consider a class of Sine-Gordon equations which arise from the model of the thermoelastic coupled rod. Firstly, by virtue of the classical semigroup theory, we prove the existence and uniqueness of the mild solution under certain initial-boundary value for above-mentioned equations. Secondly, we obtain the boundedness of solutions by the priori estimates. Lastly, we prove the existence of a global attractor.
In this paper, we consider a class of Sine-Gordon equations which arise from the model of the thermoelastic coupled rod. Firstly, by virtue of the classical semigroup theory, we prove the existence and uniqueness of the mild solution under certain initial-boundary value for above-mentioned equations. Secondly, we obtain the boundedness of solutions by the priori estimates. Lastly, we prove the existence of a global attractor.
