Asyptotics For The Solution Of Euler-Bernoulli Type Eqution

In this paper,the existence and uniqueness and the large time asymptotic behavior of the solution for the Euler-bernoulli equation with initial-value conditions are considered. By using the theory of Sobolev spaces and the contraction mapping principle,we proved that the Euler-bernoulli equation possesses a unique global solu-tion u∈C([0,∞)；Lp(Rn)∩L1,a (Rn))∩C((0,∞)；L∞(Rn)) when the initial data u0,u1∈Lp(R)∩L1.a(R)(in whichσ>1,a∈(0,1],p>σ)and its norm‖u0‖L1.a+‖u0‖Lp+‖u1‖L1.a+‖u1‖Lp is small enough.Moreover the solution u(t,x)has the following large time asymptotic behavior whereO and...