Remarks on some dissipative sine-Gordon equations

In this short note, we discuss some results concerning the long-time behaviour of solutions to dissipative sine-Gordon equation in a bounded domain of . We first prove that without forcing term and under some assumptions on the domain then the global attractor reduces to . We then rewrite the sine-Gordon equation as a Schrodinger equation with smoothing; this allows us to provide another proof for the so-called asymptotical smoothing effect for this dissipative wave equation.