【摘要】 研究如下半线性电报方程的初边值问题utt-uxx+2aut+bu=β(u2)xx,其中t>0,a,b,β是常数.当b>a2时,得到了该方程Fourier级数表示的整体解和长时间整体渐近解.更多还原

【Abstract】 In this paper, we consider an initial-boundary value problem of the following nonlinear telegraph equationu_tt-u_xx+2au_t+bu=β(u~2)_xx,where t>0, a,b, and β are constants. For the case b>a~2, we obtain a global solution of the equation in the form of Fourier series. The long time asymptotics of the global solution is found to decay exponentially in time.更多还原