Stability estimate in a Cauchy problem for a hyperbolic equation with variable coefficients
Stability estimate in a Cauchy problem for a hyperbolic equation with variable coefficients
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DOI：
10.1515/156939405775199488
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发表时间：
2005-11
期刊：
影响因子：
--
通讯作者：
O. Imanuvilov;Masahiro Yamamoto
中科院分区：
文献类型：
--
作者：
O. Imanuvilov;Masahiro Yamamoto
在有界域Ω ∞中，我们考虑主项为− p（x，t）Δ的双曲算子P。假设p的外正规导数是非正的，我们将通过<$Ω ×（−T，T）的开子集上的柯西数据来估计U ×（− t0，t0）中的u，其中t0 < T是某个常数，U是<$Ω的邻域。法向导数的条件在物理上是可以理解的，这意味着波速不会在λ Ω上向内减小。
In a bounded domain Ω ⊂ , we consider a hyperbolic operator P with the principal term − p(x,t)Δ. Under the assumption that the outer normal derivative of p is non-positive, we will estimate u in U × (−t 0, t 0) by the Cauchy data on an open subset of ∂Ω × (−T, T), where t 0 < T is some constant and U is a neighbourhood of ∂Ω. The condition on the normal derivative is physically understood and means that the wave speed does not decrease inward on ∂Ω.