A uniqueness result for a nonlinear hyperbolic equation
A uniqueness result for a nonlinear hyperbolic equation
复制标题
非线性双曲方程的唯一性结果
DOI：
10.1080/00036810701689515
复制
发表时间：
2007
影响因子：
1.1
通讯作者：
A. Lorenzi
中科院分区：
文献类型：
--
作者：
B. Kaltenbacher;A. Lorenzi
本文研究了由偏微分方程解的超定边界数据确定非线性双曲型偏微分方程主部系数函数的问题。假设系数函数可以被写为一个线性组合的许多anabolic函数，我们推导出一个稳定性和唯一性的结果，这是基于可识别的条件，在初始数据，以及在小的时间间隔。在这样做时，我们区分的二维和高维的情况下，边界上的泛函可以测量和一维的情况下，只有点测量在一个边界点。我们的结果也给前景无限维系数函数的情况下。
In this paper we consider the problem of identifying a coefficient function in the principal part of a nonlinear hyperbolic PDE from overdetermined boundary data of the PDE solution. Assuming that the coefficient function can be written as a linear combination of finitely many ansatz functions, we derive a stability and uniqueness result that is based on an identifiability condition in terms of the initial data as well as on the smallness of the time interval. In doing so, we distinguish between the two- and higher dimensional case where functionals on the boundary can be measured and the one-dimensional situation with only point measurements at one boundary point. Our results also give perspectives to the case of an infinite dimensional coefficient function.