Stability in the inverse nodal solution for the interior transmission problem

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• 作者：Chuan-Fu Yang ^{chuanfuyang@njust.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：34A55 ; 34L40 ; 35K57
• 刊名：Journal of Differential Equations
• 出版年：2016
• 出版时间：5 February 2016
• 年：2016
• 卷：260
• 期：3
• 页码：2490-2506
• 全文大小：282 K

文摘

The inverse nodal problem of determining a spherically symmetric wave speed v is considered in a bounded spherical region of radius b from zeros for eigenfunctions corresponding to the transmission eigenvalues. It is shown that the space of potential functions q   which correspond to interior transmission problems characterized by Ω:={q:q∈L²[0,1]}$\mathrm{\Omega }:=\{q:q\in L^2[0,1]\}$, under a certain metric, is homeomorphic to the partition set of the space of quasinodal sequences. As a consequence, the inverse nodal problem defined on the partition set of admissible sequence, is stable.