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Lyaponov函数与方程的指数衰减性

, PP. 504-508

Keywords: Lyaponov函数,Nehari流形,指数衰减

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Abstract:

研究了以下2类抽象发展方程解的指数衰减性.其中一类为非线性波方程utt-Δu+a∫t0g(t-τ)Δu(τ)dτ+but=u|u|p-2,另一类则为带线性记忆的双曲型方程utt+αut-k(0)Δu-∫+∞0k′(s)Δu(t-s)ds+u|u|p-2=0.利用已有的相关定理,通过构造合适的Lyaponov函数,借用一定的计算技巧从而得到以上方程解的指数衰减性结论.该结论在光学、流体力学、通信等自然科学领域具有非常重要的实际意义.

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