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强阻尼波动方程组解的性质

, PP. 649-654

Keywords: 阻尼波动方程,初边值问题,Nehari流形,位势井,稳定集,不稳定集,爆破,衰减估计

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Abstract:

运用了PotentialWell方法研究了一类强阻尼波动方程组初边值问题在Rn解的存在性,定义了该方程组的位势深度d,运用Poincaré-Soblev嵌入定理证明了位势深度d>0,再通过构建适当的能量函数E(t),稳定集和不稳定集,当初始值属于不稳定集时,解在有限时间爆破和解的衰减估计.

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