Decay of solutions for a mixture of thermoelastic solids with different temperatures

详细信息    查看全文

• 作者：Jaime E. Muñ ; oz Rivera^a ; ^b ; ^{rivera@lncc.br" class="auth_mail" title="E-mail the corresponding author} ; Maria Grazia Naso^c ; ^{mariagrazia.naso@unibs.it" class="auth_mail" title="E-mail the corresponding author} ; Ramon Quintanilla^d ; ^{ramon.quintanilla@upc.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Thermoelastic mixtures ; Exponential decay ; Weakly coupled system
• 刊名：Computers & Mathematics with Applications
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：71
• 期：4
• 页码：991-1009
• 全文大小：458 K

文摘

We study a system modeling thermomechanical deformations for mixtures of thermoelastic solids with two different temperatures, that is, when each component of the mixture has its own temperature. In particular, we investigate the asymptotic behavior of the related solutions. We prove the exponential stability of solutions for a generic class of materials. In case of the coupling matrix rc">rce" class="mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116000146&_mathId=si1.gif&_user=111111111&_pii=S0898122116000146&_rdoc=1&_issn=08981221&md5=b6f7892993945b977e44a57710584f33">rce" style="margin-top: -5px; vertical-align: middle" title="View the MathML source" src="/sd/grey_pxl.gif" data-inlimgeid="1-s2.0-S0898122116000146-si1.gif">ript>rder="0" style="vertical-align:bottom" width="11" alt="View the MathML source" title="View the MathML source" src="http://origin-ars.els-cdn.com/content/image/1-s2.0-S0898122116000146-si1.gif">ript>r hidden">roll">riant="bold">B being singular, we find that in general the corresponding semigroup is not exponentially stable. In this case we obtain that the corresponding solution decays polynomially as rc">rmulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116000146&_mathId=si2.gif&_user=111111111&_pii=S0898122116000146&_rdoc=1&_issn=08981221&md5=2c8f1464ee8fd0966e642b72acc9ca6c" title="Click to view the MathML source">t^−1/2r hidden">roll">row>trow>row>−1/2row> in case of Neumann boundary condition. Additionally, we show that the rate of decay is optimal. For Dirichlet boundary condition, we prove that the rate of decay is rc">rmulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0898122116000146&_mathId=si3.gif&_user=111111111&_pii=S0898122116000146&_rdoc=1&_issn=08981221&md5=697daf004dd0a790e417f414e4974d29" title="Click to view the MathML source">t^−1/6r hidden">roll">row>trow>row>−1/6row>. Finally, we demonstrate the impossibility of time-localization of solutions in case that two coefficients (related with the thermal conductivity constants) agree.