The Decay Estimates Of Solution For A Viscoelastic Equation With Memory Kernel In Unbounded Domain

In this paper,the energy decay estimate of solution for a viscoelastic equation with memory kernel in unbounded domain is investigated.It is proved that the energy function of system is polynomial decay when some conditions of the memory function of the equation are satisfied.In the first chapter,it gives some relevant preparatory knowledge based on this paper,including common function spaces,inequalities,definitions and theorems.In the second chapter,the Cauchy problem of the following viscoelastic equation with memory term is investigated:Where u0,u1 are given initial function,g is a nonincreasing function defined on Rn,and g is called a memory kernel.It gives the result of existence of the viscoelastic equation based on previous references,and the procedure of proof is finished by constructing appropriated auxiliary function and using integral inequalities.Besides,some results in previous references are also generalized in this paper.