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Browsing by Subject "inverse methods"

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    Item type:Article, Access status: Open Access ,
    Echoes and glimpses of a distant drum
    (Wydawnictwa AGH, 2020) Turner, John W.
    To what extent does the spectrum of the Laplacian operator on a domain $D$ with prescribed boundary conditions determine its shape? This paper first retraces the history of this problem, then Kac's approach in terms of a diffusion process with absorbing boundary conditions. It is shown how the restriction to a polygonal boundary for $D$ in this method, which required taking the limit of an infinite number of sides to obtain a smooth one, can be avoided by using the Duhamel method.