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

Zitieren

Dateien zu dieser Ressource

Dateien Größe Format Anzeige

Zu diesem Dokument gibt es keine Dateien.

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

Das Dokument erscheint in:

KOPS Suche


Stöbern

Mein Benutzerkonto