Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS

   
  Quarterly of Applied Mathematics
Quarterly of Applied Mathematics
  
Online ISSN 1552-4485; Print ISSN 0033-569X
 

   

 

Decay rates and global existence for semilinear dissipative Timoshenko systems


Authors: Reinhard Racke and Belkacem Said-Houari
Journal: Quart. Appl. Math. 71 (2013), 229-266
MSC (2010): Primary 35L71, 35B40
Published electronically: October 3, 2012
MathSciNet review: 3087421
Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We prove new decay estimates for the dissipative Timoshenko system in the one-dimensional whole space, and a global existence theorem for semilinear systems. More precisely, if we restrict the initial data $ ( (\varphi _{0},\psi _0),(\varphi _{1},\psi _1)) $ $ \in \Big ( H^{s+1}( \mathbb{R}^{N}) \cap L^{1,\gamma }( \mathbb{R}^{N}) \Big )... ... \Big ( H^{s}( \mathbb{R}^{N})\Big ) \cap L^{1,\gamma }( \mathbb{R}^{N}) \Big )$ with $ \gamma \in \left [ 0,1\right ]$, then we can derive faster decay estimates than those given by Ide, Haramoto and Kawashima. In addition, we use these decay estimates of the linear problem combined with the weighted energy method introduced by Todorova and Yordanov with the special weight given by Ikehata and Inoue to solve a semilinear problem with low regularity.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC (2010): 35L71, 35B40

Retrieve articles in all journals with MSC (2010): 35L71, 35B40


Additional Information

Reinhard Racke
Affiliation: Department of Mathematics and Statistics, University of Konstanz, 78457 Konstanz, Germany
Email: reinhard.racke@uni-konstanz.de

Belkacem Said-Houari
Affiliation: Department of Mathematics and Statistics, University of Konstanz, 78457 Konstanz, Germany
Email: belkacem.said-houari@kaust.edu.sa

DOI: http://dx.doi.org/10.1090/S0033-569X-2012-01280-8
PII: S 0033-569X(2012)01280-8
Keywords: Global existence, decay rate, Timoshenko system, semilinear wave equation
Received by editor(s): May 30, 2011
Published electronically: October 3, 2012
Article copyright: © Copyright 2012 Brown University



Brown University The Quarterly of Applied Mathematics
is distributed by the American Mathematical Society
for Brown University
Online ISSN 1552-4485; Print ISSN 0033-569X
© 2015 Brown University
Comments: qam-query@ams.org
AMS Website