The Dispersive Estimates For A Class Of Generalized Boussinesq Equations

In the present paper, we study a dispersive estimate in space Besov of the generalized IMBq(Boussinesq)equation, where u(x, t) denotes the unknown function, f(s) is some given nonlinear function, u0and u1are the given initial value functions, the subscript t indicates the partial derivative with respect to t, n is the dimension of space variable x, and△denotes the Laplace operator in Rn.The concrete content is in the following:· In section1, we introduce the background and significance of the research and the problem which we study.· In Section2, it basically presents the basic concepts, the symbols, and related lemmas, such as Fourier theory, M. Riesz interpolation theory, Littlewood-Paley theory and so on, which appear in this paper.· In Section3, it solves the linear equation with the Fourier method, and gives the point-wise estimates of this equation with the method of Oscillatory inte-gral.· In Section4, we obtain dispersive estimates of the generalized Boussinesq equation in Besov space.