On the Exponential Decay of Solutions of a Coupled System of Dissipative Benjamin–Bona–Mahony Type Equations in Domain with Moving Boundaries

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• 作者：Vanilde Bisognin ; Celene Buriol ; Marcio V. Ferreira
• 关键词：Coupled system of BBM type ; Exponential decay ; Faedo–Galerkin’s method ; 35Q99 ; 35Q53 ; 35B40
• 刊名：Acta Applicandae Mathematicae
• 出版年：2016
• 出版时间：February 2016
• 年：2016
• 卷：141
• 期：1
• 页码：49-67
• 全文大小：1,048 KB
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• 作者单位：Vanilde Bisognin (1)
  Celene Buriol (2)
  Marcio V. Ferreira (2)
  
  1. Franciscan University Center, Santa Maria, 97010-032, RS, Brazil
  2. Department of Mathematics, Federal University of Santa Maria, Santa Maria, 97105-900, RS, Brazil
  
• 刊物主题：Mathematics, general; Computer Science, general; Theoretical, Mathematical and Computational Physics; Statistical Physics, Dynamical Systems and Complexity; Mechanics;
• 出版者：Springer Netherlands
• ISSN：1572-9036

文摘

We consider the Cauchy-problem in a bounded domain with moving boundaries for the nonlinear coupled dissipative system of Benjamin–Bona–Mahony type. By means of a change of variables we reduce the problem in a cylindrical domain and study the existence and uniqueness of global solutions and prove that the total energy associated with the system decays exponentially. We combine Faedo–Galerkin’s method with arguments of compactness to study the existence of global solutions and energy estimates and multipliers techniques to obtain the exponential decay. Keywords Coupled system of BBM type Exponential decay Faedo–Galerkin’s method