Asymptotic stability of monotone increasing traveling wave solutions for viscous compressible fluid equations with capillarity term

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• 作者：Weiguo Zhang ; ^{zwgzwm@126.com" class="auth_mail" title="E-mail the corresponding author} ; Xiang Li ^{lixiang1121@yeah.net" class="auth_mail" title="E-mail the corresponding author} ; Yan Yong ^{yongyan-math@126.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Fluid equations ; Capillarity ; Monotone traveling wave ; A priori estimate ; Asymptotic stability
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：1 February 2016
• 年：2016
• 卷：434
• 期：1
• 页码：401-412
• 全文大小：422 K

文摘

Asymptotic stability of monotone increasing traveling wave solutions is investigated for a class of viscous compressible fluid equations with capillarity term. By using the theory of planar dynamical systems, the existence has been proved for the monotone increasing traveling wave solution. Moreover, through building uniformly a priori energy estimate for the perturbation of the traveling wave solution, we prove that the monotone increasing traveling wave solution is asymptotically stable in class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X15008367&_mathId=si1.gif&_user=111111111&_pii=S0022247X15008367&_rdoc=1&_issn=0022247X&md5=69fb3751f6095776d658f9fb2e2743b8" title="Click to view the MathML source">H²×H¹class="mathContainer hidden">class="mathCode">$H^2\times H^1$.