Article ID Journal Published Year Pages File Type
4609954 Journal of Differential Equations 2015 26 Pages PDF
Abstract

We study the Cauchy problem of the Ball model for an extensible beam:ρ∂t2u+δ∂tu+κ∂x4u+η∂t∂x4u=(α+β∫R|∂xu|2dx+γη∫R∂t∂xu∂xudx)∂x2u. The aim of this paper is to investigate singular limits as ρ→0ρ→0 for this problem. In the authors' previous paper [8] decay estimates of solutions uρuρ to the equation in the case ρ>0ρ>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:‖uρ−u0‖L∞([0,∞);H2(R))≤Cρ.‖uρ−u0‖L∞([0,∞);H2(R))≤Cρ.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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