该文讨论在伪欧氏空间中,带有以下初始条件的拉格朗日平均曲率流方程{ dY(x,t)dt=HY(x,0)=Y0(x)。其中,该方程等价于特殊拉格朗日抛物方程{ ∂u∂t=Fτ(D2u), t>0,x∈ℝnu=u0(x), t=0,x∈ℝn。通过构造函数,将证明若0τπ4或π4τπ2,该抛物方程存在唯一光滑解u(x,t),且存在更高阶导数的衰减估计。另一方面,应用Arzelà-Ascoli定理来获得u(x,t)收敛到拉格朗日平均曲率流方程的自膨胀解。In this paper, we consider the Lagrangian mean curvature flow equation in pseudo-Euclidean space with the initial value: { dY(x,t)dt=HY(x,0)=Y0(x). This equation is equivalent to the special Lagrangian parabolic equation { ∂u∂t=Fτ(D2u), t>0,x∈ℝnu=u0(x), t=0,x∈ℝn. By constructing a suitable function, it is proven that if 0τπ4or π4τπ2, the parabolic equation has a unique smooth solution u(x,t)and decay estimates for higher-order derivatives exist. On the other hand, the Arzelà-Ascoli theorem is applied to obtain the convergence of u(x,t)to the self-expanding solution of the Lagrangian mean curvature flow equation.