Solution to the interior transmission problem using nodes on a subinterval as input data

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• 作者：Chuan-Fu Yang^a ; ^{chuanfuyang@njust.edu.cn} ; Xiao-Chuan Xu^a ; ^{xiaochuanxu@126.com} ; Sergey Buterin^b ; ^{buterinsa@info.sgu.ru}
• 关键词：Interior transmission problem ; Inverse nodal problem ; Transmission eigenvalue
• 刊名：Nonlinear Analysis: Real World Applications
• 出版年：2017
• 出版时间：June 2017
• 年：2017
• 卷：35
• 期：Complete
• 页码：20-29
• 全文大小：601 K
• 卷排序：35

文摘

It is well known that a spherically symmetric wave speed problem in a bounded spherical region may be reduced, by means of Liouville transform, to the Sturm–Liouville problem B(a;q)B(a;q) in [0,1][0,1]. We prove that a twin dense subset of the nodal set in a subinterval (⊂[0,1]⊂[0,1]) uniquely determines the potential qq on the whole interval [0,1][0,1] and the boundary parameter aa. The method employed is to convert the inverse nodal problem into the inverse spectral problem with partial information given on the potential on a subinterval.