A Gronwall-type lemma with parameter and its application to Kirchhoff type nonlinear wave equation

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• 作者：Ke Li ; ^{like@zzu.edu.cn" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Gronwall-type inequality ; Uniform estimates ; Kirchhoff-type equations ; Global attractor
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：15 March 2017
• 年：2017
• 卷：447
• 期：2
• 页码：683-704
• 全文大小：427 K

文摘

The paper investigates a new Gronwall-type lemma with parameter n id="mmlsi1" class="mathmlsrc">n class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X16306035&_mathId=si1.gif&_user=111111111&_pii=S0022247X16306035&_rdoc=1&_issn=0022247X&md5=a18299cfb6f9f10315169290c7a3e3c1" title="Click to view the MathML source">ϵ>0n>n class="mathContainer hidden">n class="mathCode">n>n>n>, and establishes the uniform-in-time estimates. As an application, the paper studies the asymptotic behavior of the Kirchhoff-type equations with a strong dissipation, and proves that the related solution semigroup possesses the global attractor.