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Singular limits in the Cauchy problem for the damped extensible beam equation

Singular limits in the Cauchy problem for the damped extensible beam equation

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RACKE, Reinhard, Shuji YOSHIKAWA, 2015. Singular limits in the Cauchy problem for the damped extensible beam equation. In: Journal of Differential Equations. 259(4), pp. 1297-1322. ISSN 0022-0396. eISSN 1090-2732. Available under: doi: 10.1016/j.jde.2015.02.045

@article{Racke2015Singu-31284, title={Singular limits in the Cauchy problem for the damped extensible beam equation}, year={2015}, doi={10.1016/j.jde.2015.02.045}, number={4}, volume={259}, issn={0022-0396}, journal={Journal of Differential Equations}, pages={1297--1322}, author={Racke, Reinhard and Yoshikawa, Shuji} }

eng 2015-06-25T08:08:42Z Racke, Reinhard Yoshikawa, Shuji We study the Cauchy problem of the Ball model for an extensible beam:<br />ρ∂<sup>2</sup><sub>t</sub>u+δ∂<sub>t</sub>u+κ∂<sup>4</sup><sub>x</sub>u+η∂<sub>t</sub>∂<sup>4</sup><sub>x</sub>u=(α+β∫<sub>R</sub>|∂<sub>x</sub>u|<sup>2</sup>dx+γη∫<sub>R</sub>∂<sub>t</sub>∂<sub>x</sub>u∂<sub>x</sub>udx)∂<sup>2</sup><sub>x</sub>u.<br /><br />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 uρuρ 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:<br />‖uρ−u0‖L∞([0,∞);H2(R))≤Cρ . 2015-06-25T08:08:42Z Singular limits in the Cauchy problem for the damped extensible beam equation 2015 Yoshikawa, Shuji Racke, Reinhard

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