Structural Stability for a Class of Nonlinear Wave Equations

Authors : Ülkü DİNLEMEZ

Pages : 83-87

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Publication Date : 2010-03-22

Article Type : Other Papers

Abstract :In this paper we discuss the structural stability of an initial value problem defined for the equation   u t -u txx + a uu x = b u x u xx +uu xxx                                                                      insert ignore into journalissuearticles values(i.1);   where   a , b are constants, x Ğ„ ℝ , t Ğ„ ℝ .   For the choices of a and b , insert ignore into journalissuearticles values(i.1); describe the nonlinear shallow water waves. Upper and lower bounds are derived for energy decay rate in every finite interval [0, T ] which reveals that only the lower bound of the energy decays exponentially.   Key Words : Degasperis-Procesi equation, Camassa-Holm equation, traveling wav e    
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