- Gazi University Journal of Science
- Vol: 22 Issue: 2
- Structural Stability for a Class of Nonlinear Wave Equations
Structural Stability for a Class of Nonlinear Wave Equations
Authors : Ülkü Dinlemez
Pages : 83-87
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Publication Date : 2010-03-22
Article Type : Other
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 (i.1) where a , b are constants, x Ğ â , t Ğ â . For the choices of a and b , (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 eKeywords :