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- W2000848014 abstract "We study the Cauchy problem of the Ball model for an extensible beam: ρ ∂ t 2 u + δ ∂ t u + κ ∂ x 4 u + η ∂ t ∂ x 4 u = ( α + β ∫ R | ∂ x u | 2 d x + γ η ∫ R ∂ t ∂ x u ∂ x u d x ) ∂ x 2 u . The aim of this paper is to investigate singular limits as ρ → 0 for this problem. In the authors' previous paper [8] decay estimates of solutions u ρ to the equation in the case ρ > 0 were shown. With the help of the decay estimates we describe the singular limit in the sense of the following uniform (in time) estimate: ‖ u ρ − u 0 ‖ L ∞ ( [ 0 , ∞ ) ; H 2 ( R ) ) ≤ C ρ ." @default.
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- W2000848014 date "2015-08-01" @default.
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- W2000848014 title "Singular limits in the Cauchy problem for the damped extensible beam equation" @default.
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- W2000848014 doi "https://doi.org/10.1016/j.jde.2015.02.045" @default.
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