BOUSSINESQ EQUATION IN ELASTIC RODS.

Abstract

In this project, the goal is to consider the equation of the transverse deflections of the rod when it is firmly connected to an elastic foundation. We study the well-posedness of the corresponding Cauchy problem, that is, existence, uniqueness and persistence properties of the solutions inherit by the initial data. Moreover, we will also find the conditions under which the solutions can extend globally in time in $L^2$ and the energy space $X$. Furthermore, we establish the persistence decay properties of the solutions in $X^s$.