L2-estimates of solutions for damped wave equations with space-time dependent damping term

Jiayun Lin, Kenji Nishihara, Jian Zhai

    研究成果: Article査読

    17 被引用数 (Scopus)

    抄録

    In this paper, we consider the damped wave equation with space-time dependent potential b (t, x) and absorbing semilinear term | u |ρ - 1 u. Here, b (t, x) = b0 (1 + | x |2)- frac(α, 2) (1 + t)- β with b0 > 0, α, β ≥ 0 and α + β ∈ [0, 1). Based on the local existence theorem, we obtain the global existence and the L2 decay rate of the solution by using the weighted energy method. The decay rate coincides with the result of Nishihara [K. Nishihara, Decay properties for the damped wave equation with space dependent potential and absorbed semilinear term, preprint] in the case of β = 0 and coincides with the result of Nishihara and Zhai [K. Nishihara, J. Zhai, Asymptotic behaviors of time dependent damped wave equations, preprint] in the case of α = 0.

    本文言語English
    ページ(範囲)403-422
    ページ数20
    ジャーナルJournal of Differential Equations
    248
    2
    DOI
    出版ステータスPublished - 2010 1 15

    ASJC Scopus subject areas

    • Analysis

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