Long-time Dynamics Of A Quasi-linear Strongly Damped Membrane Equation

The paper studies the well-posedness of the global solution and the existence of global and exponential attractor for a quasi-linear strongly damped membrane equationIt proves that the global attractor of the equation has the further regularity and the IBVP of the equation has an exponential attractor. We present a new functional analysis method of constructing the bounded absorbing set with higher whole regularity (rather than the long-standing partially regularity). This method allows us to use the weak quasi-stability estimates (rather than the strong one as usual) to establish an exponential attractor (rather than a weak one) in natural energy space. The results improve the recent one achieved by Kalantarov and Zelik.