On asymptotic properties of solutions to σ-evolution equations with general double damping

2023/11/11 by Dao, Tuan Anh, Van Duong, Dinh, Nguyen, Duc Anh
#35B40 #35B44 #35L30 #35L56 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2311.06660

Abstract

In this paper, we would like to consider the Cauchy problem for semi-linear σ-evolution equations with double structural damping for any σ≥ 1. The main purpose of the present work is to not only study the asymptotic profiles of solutions to the corresponding linear equations but also describe large-time behaviors of globally obtained solutions to the semi-linear equations. We want to emphasize that the new contribution is to find out the sharp interplay of ``parabolic like models" corresponding to σ<sub>1</sub> ∈ [0,σ/2) and ``σ-evolution like models" corresponding to σ₂ ∈ (σ/2,σ], which together appear in an equation. In this connection, we understand clearly how each damping term influences the asymptotic properties of solutions.

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