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arXiv · 1912.10181

Singular limit problem of abstract second order evolution equations

Ryo Ikehata·Motohiro Sobajima
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Abstract

We consider the singular limit problem in a real Hilbert space for abstract second order evolution equations with a parameter $\varepsilon \in (0,1]$. We first give an alternative proof of the celebrated results due to Kisynski (1963) from the viewpoint of the energy method. Next we derive a more precise asymptotic profile as $\varepsilon \to +0$ of the solution itself depending on $\varepsilon$ under rather high regularity assumptions on the initial data.

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Ryo Ikehata, Motohiro Sobajima. 2019-12-21. Singular limit problem of abstract second order evolution equations. https://arxiv.org/abs/1912.10181

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