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Inverse Nodal Problems: Finding the Potential from Nodal Lines
Ole H. HaldJoyce McLaughlin
其他書名
Finding the Potential from Nodal Lines
出版American Mathematical Soc., 1996
主題Mathematics / GeneralMathematics / Matrices
ISBN08218048639780821804865
URLhttp://books.google.com.hk/books?id=MXzTCQAAQBAJ&hl=&source=gbs_api
EBookSAMPLE
註釋In this paper we consider an eigenvalue problem which arises in the study of rectangular membranes. The mathematical model is an elliptic equation, in potential form, with Dirichlet boundary conditions. We show that the potential is uniquely determined, up to an additive constant, by a subset of the nodal lines of the eigenfunctions. A formula is shown which, when the additive constant is given, yields an approximation to the potential at a dense set of points. We present an estimate for the error made by the formula. A substantial part of this work is the derivation of the asymptotic forms for a rich set of eigenvalues and eigenfunctions for a large set of rectangles.