Existence and Continuous Dependence of the Local Solution of a Non-Homogeneous Equation of Order Multiple of Four

Abstract

In this article, we prove that initial value problem associated to the non- homogeneous n-th order equation in periodic Sobolev spaces with n multiple of four has a local solution in [0, T] with T > 0, and the solution has continuous dependence with respect to the initial data and the non-homogeneous part of the problem. We do this in a intuitive way using Fourier theory and introducing a - Semigroup inspired by the work of Iorio [1] and Santiago [5].