变系数耗散波动方程的能量衰减估计

研究了在（0，∞）×Rⁿ上，变系数耗散波动方程的能量在外区域上的衰减估计，得到：若初值{u₀，u₁}属于能量空间且具有紧支集，则在Rⁿ上存在一个外区域X_m，使得对任意t ≥ 0和m>0，有进一步，若u₀+u₁=0，还可以得到∫_Xm|u|²dx ≤ C（1+t）^-m，t ≥ 0.

Energy decay for a dissipative wave equation with variable coefficients

In this paper, we study the energy decay estimates to the Cauchy problem of dissipative wave equation with variable coefficients:u_tt-?_xi(a^ij(x)?_xju)+u_t=0. If the initial data {u₀, u₁} are compactly supported from the energy space, then there exists a exterior domain X_m?Rⁿ such that for large t ≥ 0, we have ∫_Xm(|u_t|²+a^ij(x)u_xiu_xj)dx ≤ C(1+t)^-m with m>0. Moreover, if u₀+u₁=0, we also have ∫_Xm|u|²dx ≤ C(1+t)^-m for t ≥ 0.