R^n空间中带有密度函数的四阶粘弹方程的一致衰减性

Uniform Decay for a Fourth-Order Viscoelastic Equation with Density in R^n

该文研究了一个R^n(n≥4)空间中带有密度函数的四阶粘弹方程.为了弥补Poincaré不等式在R^n空间中的不足,作者引入了一个加权空间.在对松弛函数适当的假设下,作者利用能量扰动的方法建立了初边值问题解的一致衰减性结果,并且该结果推广了前人的结果.

In this paper, we investigate a fourth-order linear viscoelastic equation with den- sity in the whole space R^n （n 〉 4）. To compensate the lack of Poincare＇s inequality in R^n, we consider the solutions in weighted spaces. Under suitable assumptions on the relaxation function, we establish a general decay result of solution for the initial value problem by using energy perturbation method. Our result extends earlier results.