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  8. Checklist for Project Paper MATH 401/801 : 2012

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    Smith, Gregory G.

    1 2 3 4 5 2 Examples: Relevant examples enrich the central theme. Each theorem is illustrated the reader through the text. 0 1 2 3 4 5 2 Conventions: The write demonstrates a good grasp of standard

  9. Self-Similar Blowup Solutions to the 2-Component Degasperis-Procesi Shallow Water System

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    Manwai Yuen

    2010-08-13

    In this article, we study the self-similar solutions of the 2-component Degasperis-Procesi water system:% [c]{c}% \\rho_{t}+k_{2}u\\rho_{x}+(k_{1}+k_{2})\\rho u_{x}=0 u_{t}-u_{xxt}+4uu_{x}-3u_{x}u_{xx}-uu_{xxx}+k_{3}\\rho\\rho_{x}=0. By the separation method, we can obtain a class of self-similar solutions,% [c]{c}% \\rho(t,x)=\\max(\\frac{f(\\eta)}{a(4t)^{(k_{1}+k_{2})/4}},\\text{}0),\\text{}u(t,x)=\\frac{\\overset{\\cdot}{a}(4t)}{a(4t)}x \\overset{\\cdot\\cdot}{a}(s)-\\frac{\\xi}{4a(s)^{\\kappa}}=0,\\text{}a(0)=a_{0}% \