Well-posedness For A Class Of Plate Equations With Degenerate Damping Term

In this paper,we focus on the existence,asymptotics and blow-up of solutions for a class of initial boundary value problems of plate equations with nonlocally degenerate damping as follows:#12 where Ω is a bounded domain in Rn(n≥1)with sufficiently smooth boundary,u0(x)and u1(x)are given initial datas.The parameter p satisfies 2<p≤2(n-2)/(n-4),n≥5;2<p<∞,n≤4.In the paper,by using semigroup theory,potential well theory,the continuous extension theorem and Nakao’s inequality,we establish the existence of the local solution,the existence of the global solution and the decay estimation when the initial data is in a stable set.Finally,for this plate equation with degenerate damping term,we prove the blow-up results and the estimation of the blow-up time for solution when initial energy 0<E(0)<d and E(0)<0.We also obtain the existence of certain solutions which blow up in finite time for initial data at arbitrary energy level.Moreover,an lower bound of the blow-up time is established when the solution blow up.