Uniform energy decay for wave equations with unbounded damping coefficients

2017/06/13 by Ryo Ikehata, Ikehata, Ryo, Hiroshi Takeda +1
Computer Science · Engineering · Mathematics · #35B35 #35B40 #35L05 #Advanced Mathematical Modeling in Engineering #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1706.03942

openalex publication_date 2017/06/13 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Cauchy problem for wave equations with unbounded damping coefficients in the whole space. For a general class of unbounded damping coefficients, we derive uniform total energy decay estimates together with a unique existence result of a weak solution. In this case we never impose strong assumptions such as compactness of the support of the initial data. This means that we never rely on the finite propagation speed property of the solution, and we try to deal with an essential unbounded coefficient case.

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