Asymptotic Behavior Of Solution Of Kirchhoff-type Equation

In this paper,we consider the asymptotic behavior of Kirchhoff-type equation. By research,we find that the solution behave as a solution to the parabolic equation. Kirchhoff-type equation like this, Vtt-(1+||V||2Vxx+Vt=0,(x,t)∈R×(0,∞), V(0,·)=V0, Vt(0,.)=V1 heat equatiOn is, φt-φxx=0, φ(0,·)=V0+V1.Then,the solution V of the hyperbolic equation and the solution φ of heat equation satisfies. ||V-φ||L∞≤C(1+t)-5/4�'(1+t).