Singular limit problem of abstract second order evolution equations

2019/12/21 by Ryo Ikehata, Ikehata, Ryo, Motohiro Sobajima +1
Computer Science · Mathematics · #34G10 #34K26 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #Differential Equations and Numerical Methods #FOS: Mathematics #Functional Analysis (math.FA) #Nonlinear Differential Equations Analysis

paper · pdf · doi:10.48550/arxiv.1912.10181

openalex publication_date 2019/12/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the singular limit problem in a real Hilbert space for abstract second order evolution equations with a parameter ε ∈ (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 ε → +0 of the solution itself depending on ε under rather high regularity assumptions on the initial data.

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