Uniform rates of decay in nonlinear viscoelasticity for polynomial decaying kernels

Abstract

We prove a global existence theorem for the nonlinear viscoelastic equation for small data in and that the solution decays algebraically to zero when the kernel decays also algebraically as t goes to infinity. That is, if the kernel g satisfies

with p > 2, then the firts and second order energy decay as .

Keywords:

• viscoelasticity
• global situationexponential and polynomial decay
• initial boundary value problems

^*Partially supported by a grant of CNPq-BRASIL

^†Partially supported by a grant of CNPq-BRASIL

^*Partially supported by a grant of CNPq-BRASIL

^†Partially supported by a grant of CNPq-BRASIL

Notes

^*Partially supported by a grant of CNPq-BRASIL

^†Partially supported by a grant of CNPq-BRASIL