Decay rates and global existence for semilinear dissipative Timoshenko systems

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2010
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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((φ00), (φ1, Ψ1)) ∈ (Hs+1 (ℝN) ∩ L1,γ(ℝN)) X (Hs(ℝN) ∩ L1,γ(ℝN)) 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.

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ISO 690RACKE, Reinhard, Belkacem SAID-HOUARI, 2010. Decay rates and global existence for semilinear dissipative Timoshenko systems
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@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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