Global existence for nonlinear elastic waves in high space dimensions

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• 作者：Weimin Peng ; ^{weiminpeng7@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Weiguo Zhang ; ^{zwgzwm@126.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：35L52 ; 35L72
• 刊名：Nonlinear Analysis
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：148
• 期：Complete
• 页码：203-211
• 全文大小：605 K

文摘

In Georgiev et al. (2005), the authors proved the global existence of solutions to the Cauchy problem of nonlinear elastic waves with memory for space dimensions class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X16302140&_mathId=si1.gif&_user=111111111&_pii=S0362546X16302140&_rdoc=1&_issn=0362546X&md5=cc8063821849628c288c5067cb729169" title="Click to view the MathML source">n≥3class="mathContainer hidden">class="mathCode">$n\ge 3$. In this manuscript, we show that in high space dimensions class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0362546X16302140&_mathId=si2.gif&_user=111111111&_pii=S0362546X16302140&_rdoc=1&_issn=0362546X&md5=ef31f5319bc77adbb90be0e9c24256df" title="Click to view the MathML source">n≥4class="mathContainer hidden">class="mathCode">$n\ge 4$, even without such memory effect, global solutions can be also constructed. The main tool we used is the vector fields method adapted to elastic waves in Sideris’s work (Sideris, 2000).