Asymptotics of the global solutions for a nonlinear telegraph equation

Abstract

In this paper, we consider an initial-boundary value problem for the following nonlinear telegraph equation Utt - U xx + 2au, + bu = f3(u 2 )xx, where t > 0, a, band (3 are constants. For the case b > a2 , we establish a global solution of the equation in the form of a Fourier series. The coefficients of the series are related to a small parameter present in the initial conditions and are expressed as uniformly convergent series of the parameter. The long time asymptotics of the global solution is found to decay exponentially in time.