Asymptotic Profile Of Solutions To The Generalized Double Dispersion Equation

In this paper,we investigate the initial value problem for the generalized double dispersion equation in R~n.Firstly,decay estimate and asymptotic profiles of solutions to the corresponding linear problem are established.The asymptotic profiles of solution to the corresponding linear problem is given by the the convolution of the fundamental solutions of heat and free wave equation.Secondly,asymptotic profiles of solutions established show the decay estimate of solutions to the corresponding linear problem obtained is optimal in this paper.Finally,global existence and decay estimate of solutions to the nonlinear problem are established.