Inverse problems and sharp eigenvalue asymptotics for Euler-Bernoulli operators

2013/09/13 by Andrey Badanin, Badanin, Andrey, Evgeny Korotyaev +1
Computer Science · Mathematics · Physics and Astronomy · #34L20 #47E05 #Advanced Mathematical Modeling in Engineering #Analytic and geometric function theory #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #math-ph #math.MP #msc:34L20 #msc:47E05

paper · pdf · doi:10.48550/arxiv.1309.3449

33 pages

openalex publication_date 2013/09/13 · arxiv created 2014/12/16 · arxiv updated 2014/12/17 · openalex created_date 2022/10/04 · openalex updated_date 2026/07/28

Abstract

We consider Euler-Bernoulli operators with real coefficients on the unit interval. We prove the following results: i) Ambarzumyan type theorem about the inverse problems for the Euler-Bernoulli operator. ii) The sharp asymptotics of eigenvalues for the Euler-Bernoulli operator when its coefficients converge to the constant function. iii) The sharp eigenvalue asymptotics both for the Euler-Bernoulli operator and fourth order operators (with complex coefficients) on the unit interval at high energy.

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