A stiff problem: stationary waves and approximations. (English) Zbl 07215938
Constanda, Christian (ed.) et al., Integral methods in science and engineering. Analytic treatment and numerical approximations. Based on talks given at the 15th international conference on integral methods in science and engineering, IMSE, Brighton, UK, July 16–20, 2018. Basel: Birkhäuser. 133-148 (2019).
Summary: In this paper we revisit a Stiff problem which deals with the asymptotic behavior of the eigenvalues and eigenfunctions of a problem for the Laplace operator posed in a domain \(\Omega\) of \(\mathbb{R}^N\): this domain is composed of two parts in which the stiffness constants are of different order of magnitude, namely, \(O(\varepsilon)\) and O(1), respectively, where \(\varepsilon\) is a parameter \(\varepsilon\ll 1\). Here, for each fixed \(\varepsilon\), we give explicit formulas for the eigenvalues and the eigenfunctions, while, as \(\varepsilon\rightarrow 0\), we provide approaches to solutions of the associated evolution problem via “standing waves.”
For the entire collection see [Zbl 1417.65006].
For the entire collection see [Zbl 1417.65006].
MSC:
| 47Axx | General theory of linear operators |
| 34Lxx | Ordinary differential operators |
| 47Exx | Ordinary differential operators |
| 65Lxx | Numerical methods for ordinary differential equations |
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