Structural Stability for a Class of Nonlinear Wave Equations

Abstract

In this paper we discuss the structural stability of an initial value problem defined for the equation

 

u_t-u_txx+auu_x=bu_xu_xx+uu_xxx                                                                    (i.1)

 where  a, b are constants, x Ğ„ ℝ , t Ğ„ ℝ.  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 wave

 

 

Keywords

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References

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