In this paper,the existence,the uniqueness,the asymptotic behavior and the non-existence of the global generalized solutions of the initial boundary value problems for the non-linear pseudo-parabolic equation ut-αuxx-βuxxt=F（u）-βF （u）xx are proved,where α,β 0 are constants,F（s） is a given function.
The decay estimations of the solution to an elliptic equation with dynamical boundary condition is considered.We proved that,for suitable initial datum,the energy of the solution decays "in time" exponentially if p=0,whereas the decay is polynomial order if p>0.
