【摘要】 研究了在有界区间(0,L)上一维非线性波动方程的渐进性,当阻尼函数a(x)在有界区间(0,L)R1上可以变号并且满足a-=1L∫0La(x)dx>0时,证明了方程在以下两种情况下能够指数衰减:(i)a∈L∞并且非线性函数f满足整体Lipschitz连续;(ii)‖a-a-‖L∞充分小,以及函数f满足增长性条件.更多还原

【Abstract】 Asymptotic behavior for one dimensional nonlinear wave equation in(0,L) is studied,when damping function a(x) which is defined in(0,L)R1,could change sign and satisfy a=1L∫ L0a(x)dx>0,we prove the exponential decay for the solution in the following two cases:(i) a∈L∞ and f satisfy global Lipschitz condition;(ii) ‖a-a‖L∞ is small enough and f satisfy some growth condition.更多还原