Worcester Polytechnic Institute Electronic Projects Collection

Title page for E-project-050208-143730

Project TypeMQP
Submission date2008-05-02
Author
  • Eyuel D Abebe, eyueld@WPI.EDU, MA
    • URNE-project-050208-143730
    TitleQualitative Behavior of Solutions For Shallow Water Wave
    Advisor
  • Luo, Tao, MA
    • Availability unrestricted

    Abstract

    This MQP report concerns the finding

    of the convergence rates to the equilibrium constant states of

    shallow water wave equations with relaxation as time goes to

    infinity and establishing the existence of global in time solutions.

    We study the initial value problem, under a certain set of initial

    conditions, by considering the system in Lagrangian coordinates

    using different transformations. We develop two essential lemmas that we employ to

    prove the global in time existence of solutions and show, moreover,

    how these lemmas yield the convergence rates, given the initial

    conditions. We also look at the general case by strengthening the

    initial conditions and arrive at another system of equations that is

    similar to the previous one, the analysis of which follows

    naturally.

    Files
  • FINALMQP.pdf

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