Decay rates and global existence for semilinear dissipative Timoshenko systems

Racke, Reinhard; Said-Houari, Belkacem

Decay rates and global existence for semilinear dissipative Timoshenko systems

Files

timors_2.pdf(465.67 KB)

Date

2010

Authors

Racke, Reinhard

Said-Houari, Belkacem

Series

Konstanzer Schriften in Mathematik; 274

Publication type

Working Paper/Technical Report

Abstract

The main goal of this paper is to prove optimal decay estimates for the dissipative Timoshenko system in the one-dimensional whole space, and to prove a global existence theorem for semilinear systems. More precisely, if we restrict the initial data((φ₀,Ψ₀), (φ₁, Ψ₁)) ∈ (H^s+1 (ℝ^N) ∩ L^1,γ(ℝ^N)) X (H^s(ℝ^N) ∩ L^1,γ(ℝ^N)) with γ∈ [0,1], then we can derive faster decay estimates than those known before. Then, we use these decay estimates of the linear problem combined with the weighted energy method introduced by Todorova and Yordanov with the special to tackle a semilinear problem.

Subject (DDC)

510 Mathematics

Cite This

ISO 690

RACKE, Reinhard, Belkacem SAID-HOUARI, 2010. Decay rates and global existence for semilinear dissipative Timoshenko systems

BibTex

@techreport{Racke2010Decay-12345,
  year={2010},
  series={Konstanzer Schriften in Mathematik},
  title={Decay rates and global existence for semilinear dissipative Timoshenko systems},
  number={274},
  author={Racke, Reinhard and Said-Houari, Belkacem}
}

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    <dcterms:abstract xml:lang="eng">The main goal of this paper is to prove optimal decay estimates for the dissipative Timoshenko system in the one-dimensional whole space, and to prove a global existence theorem for semilinear systems. More precisely, if we restrict the initial data((&amp;#966;&lt;sub&gt;0&lt;/sub&gt;,&amp;#936;&lt;sub&gt;0&lt;/sub&gt;), (&amp;#966;&lt;sub&gt;1&lt;/sub&gt;, &amp;#936;&lt;sub&gt;1&lt;/sub&gt;)) &amp;#8712; (H&lt;sup&gt;s+1&lt;/sup&gt; (&amp;#8477;&lt;sup&gt;N&lt;/sup&gt;)	&amp;#8745;  L&lt;sup&gt;1,&amp;#947;&lt;/sup&gt;(&amp;#8477;&lt;sup&gt;N&lt;/sup&gt;)) X (H&lt;sup&gt;s&lt;/sup&gt;(&amp;#8477;&lt;sup&gt;N&lt;/sup&gt;) &amp;#8745; L&lt;sup&gt;1,&amp;#947;&lt;/sup&gt;(&amp;#8477;&lt;sup&gt;N&lt;/sup&gt;)) with &amp;#947;&amp;#8712; [0,1], then we can derive faster decay estimates than those known before. Then, we use these decay estimates of the linear problem combined with the weighted energy method introduced by Todorova and Yordanov with the special to tackle a semilinear problem.</dcterms:abstract>
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