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.