Inverse Hyperbolic Problems with Time-Dependent Coefficients
Inverse Hyperbolic Problems with Time-Dependent Coefficients
复制标题
具有瞬态系数的反双曲问题
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
G. Eskin
中科院分区：
文献类型：
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作者：
G. Eskin
考虑Rn中有界区域上的二阶自伴双曲型方程的反问题，其中低阶项解析地依赖于时间变量。我们证明，假设BLR条件下，时间依赖的Dirichlet-诺依曼算子规定的边界的一部分，唯一确定的双曲方程的系数，直到一个规范变换和一个规范同态。作为副产品，我们证明了一个类似的结果，非自伴双曲型算子与时间无关的系数。
We consider the inverse problem for the second order self-adjoint hyperbolic equation in a bounded domain in R n with lower order terms depending analytically on the time variable. We prove that, assuming the BLR condition, the time-dependent Dirichlet-to-Neumann operator prescribed on a part of the boundary uniquely determines the coefficients of the hyperbolic equation up to a diffeomorphism and a gauge transformation. As a by-product we prove a similar result for the nonself-adjoint hyperbolic operator with time-independent coefficients.