一类具有记忆项的双曲型方程解的能量衰减估计

Decay Estimate of Energy for the Solution of Hyperbolic Equation with Memory

讨论了一类带记忆项的双曲型的阻尼波动方程解的能量衰减估计问题.此类方程的损耗十分微弱,且包含在记忆项中.利用乘子思想,构造等价于能量函数E(t)的Lyapunov函数L并利用微分不等式来得到相应的解的能量衰减估计.

In this paper,we discuss the energy attenuation estimation problem for a class of hyperbolic damped wave equations with memory terms.The loss of such equations is very weak and is included in the memory terms. We use the idea of multipliers to construct a function that is equivalent to the energy of system E（ t） of a Lyapunov function L（ t） and obtain the energy attenuation estimation of the corresponding solution by using the differential inequality.