Energy Decay Properties Of Two Kinds Of Partial Differential Equations With Internal Friction

In this paper, we consider the solution to the problem of the viscoelastic equation with damping: and the second order evolution equation with abstract operator: As for the first problem, we establish an exponential decay rate result by using some auxiliary functionals under appropriate assumptions on g. As for the second problem, we get a general decay result of the energy for the second order evolution equation with abstract operator by applying general methods. Here, the exponential decay result and polynomial decay result are only two special cases.