A uniqueness theorem for second order hyperbolic differential equations
A uniqueness theorem for second order hyperbolic differential equations
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二阶双曲微分方程的唯一性定理
DOI：
10.1080/03605309208820860
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发表时间：
1992
影响因子：
1.9
通讯作者：
H. Lars
中科院分区：
文献类型：
--
作者：
H. Lars
如果u ∈ H&（（-T，T）x 0）满足方程Pu= 0，并且对于某个xo ∈ 0，u在（-T，T）x（so）的某个邻域中为零，Robbiano证明了u在（1.2）{（t，a）E（-T，T）x 0;其中d（x，x 0）是在对应于A的黎曼度量中从x到x 0的距离，并且K是仅取决于C1和C2的常数。也很容易消除这种依赖。实际上，如果A被正倍数XA代替，则Cj被XC代替，并且由于XP= Di-XA（x，Di），其中t= t/&，我们得出结论：
If u E H& ((-T, T) x 0) satisfies the equation Pu= 0 and vanishes in some neighborhood of (-T, T) x {so) for some xo E 0, Robbiano proved that u must vanish in (1.2){(t, a) E (-T, T) x 0;(tJ+ Kd (x, 20)< T} where d (x, xo) is the distance from x to xo in the Riemannian metric corresponding to A and K is a constant depending only on C1 and C2. It is easy to remove this dependence also. In fact, if A is replaced by a positive multiple XA, then Cj is replaced by XC,, and since XP= Di-XA (x, D,), where t= t/&, we conclude that solutions of