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    NEUMANN-BOUNDARY STABILIZATION OF THE WAVE EQUATION WITH INTERNAL DAMPING CONTROL AND APPLICATIONS

    NEUMANN-BOUNDARY STABILIZATION OF THE WAVE EQUATION WITH INTERNAL DAMPING CONTROL AND APPLICATIONS. Masters thesis, King Fahd University of Petroleum and Minerals.

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    Arabic Abstract

    هذه الاطروحة تكرس الاستقرار الحيدي لمعادلة الامواج غير المتجانسة في البعد n والتي تخضع للشروط الحدية السكونية والديناميكية باستخدام قانون التغذية الراجعة الخطي الذي ينطوي فقط على الحد التخامدي. نقدم طريقة بسيطة لنحصل على تقارب للحلول في الأنظمة التي يتم دراستها من خلال تقديم معيار طاقة جديد. وأخيراً، الطريقة المعروضة في هذا العمل تطبق على عدة أنظمة مثل نظام بيتروفسكي، معادلات موجة-موجة ، وأنظمة المرونة.

    English Abstract

    This thesis is devoted to the Neumann boundary stabilization of a nonhomogeneous n-dimensional wave equation subject to static or dynamic boundary conditions. Using a linear feedback law involving only an internal term, we prove the well-posedness of the considered systems and provide a simple method to obtain an asymptotic convergence result for the solutions. The method consists of proposing a new energy norm, and applying the semigroup theory and LaSalle’s principle. Finally, the method presented in this work is also applied to several distributed parameter systems such as the Petrovsky system, coupled wave-wave equations and elastic system.

    Item Type: Thesis (Masters)
    Subjects: Seminars
    Math
    Physics
    Department: College of Computing and Mathematics > Mathematics
    Committee Advisor: Guesmia, Aissa
    Committee Members: Bokhari, Ashfaque and Messaoudi, Salim and Mustafa, Mohammad and Tatar, Nasser-eddine
    Depositing User: MARABEH SAED ALI (g201202700)
    Date Deposited: 02 Jun 2014 07:07
    Last Modified: 01 Nov 2019 15:42
    URI: http://eprints.kfupm.edu.sa/id/eprint/139194