L²-growth property for wave equations with higher derivative terms

2023/07/25 by Ryo Ikehata, Xiaoyan Li, Ikehata, Ryo +1
Mathematics · #35B40 #35C20 #35E15 #35L05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2307.13329

openalex publication_date 2023/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Cauchy problems in the whole space for wave equations with higher derivative terms. We derive sharp growth estimates of the L²-norm of the solution itself in the case of the space 1, 2 dimensions. By imposing the weighted L¹-initial velocity, we can get the lower and upper bound estimates of the solution itself. In three or more dimensions, we observe that the L²-growth behavior of the solution never occurs in the (L² ∩ L¹)-framework of the initial data.

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