Singular limit problem of abstract second order evolution equations
Ryo Ikehata, Motohiro Sobajima · Hokkaido Mathematical Journal · 2023
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 [10] 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 a suitable regularity of the initial data.