Type of Publication: | Working Paper/Technical Report |
URI (citable link): | http://nbn-resolving.de/urn:nbn:de:bsz:352-0-264314 |
Author: | Racke, Reinhard; Yoshikawa, Shuji |
Year of publication: | 2014 |
Series: | Konstanzer Schriften in Mathematik ; 334 |
Summary: |
We study the Cauchy problem of the Ball model for an extensible beam: \[\rho \partial_t^2 u + \delta \partial_t u + \kappa \partial_x^4 u + \eta \partial_t \partial_x^4 u = \left(\alpha + \beta \int_{\R} |\partial_x u|^2 dx + \gamma \eta \int_{\R} \partial_t \partial_x u \partial_x u dx \right) \partial_x^2 u.\]. The aim of this paper is to investigate singular limits as $\rho \to 0$ for this problem. In the authors' previous paper \cite{ra-yo} decay estimates of solutions $u_{\rho}$ to the equation in the case $\rho>0$ were shown. With the help of the decay estimates we describe the singular limit in the sense of the following uniform (in time) estimate: \[\| u_{\rho} - u_{0} \|_{L^{\infty}([0,\infty); H^2(\R))} \leq C \rho.\]
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Subject (DDC): | 510 Mathematics |
Link to License: | In Copyright |
Bibliography of Konstanz: | Yes |
RACKE, Reinhard, Shuji YOSHIKAWA, 2014. Singular limits in the Cauchy problem for the damped extensible beam equation
@techreport{Racke2014Singu-30729, series={Konstanzer Schriften in Mathematik}, title={Singular limits in the Cauchy problem for the damped extensible beam equation}, year={2014}, number={334}, author={Racke, Reinhard and Yoshikawa, Shuji} }
Racke_0-264314.pdf | 305 |