In this paper,we mainly consider the large time behavior of global solutions to the Cauchy problem of fourth order parabolic equation in one dimension space:with f(u) satisfyingHere are our main results:(i) Suppose the initial data satisfies .and its norms are sufficiently small, we establish the time-decay rate of global solution in Lp-norm :Also , we can prove that for q > 2,the large time behavior of global solution,inLP(R)(1 < p ≤∞), is described by U = et(△-△)u0:Here U = et(△-△)u0 is the solution of the following homogeneous equation with initial data u0which satisfies the following estimates(ii) Moreover,for the case p = 1,we suppose :Here,Iβ is the Riesz Potential,which satisfies Iβu0=C(?)R|x-y|β-1u0(y)dy. Under these assumption ,We have the L1-decay rate of the solution to equation (0.9):thenthenThis is the first result about L1-decay to fourth order parabolic equation.Remark 1: We emphasis q > 2 and the smallness of initial data in the above results .For the case 1 < q ≤ 2 and the general initial data ,it remains to be considered.Remark 2: The method developed in this paper can also be used to consider the high dimensional case ,and to consider the large time behavior of global solution to fourth order parabolic equation with second order homogeneous parts, such as... |