Wellposedness of a Cauchy Problem Associated to the Even Order Equation

Abstract

In this article we prove that the Cauchy problem associated to n-th order equation in periodic Sobolev spaces is globally well posed when n is an even number multiple of four. We do this in an intuitive way using Fourier theory and in a fine version using semigroups theory. Finally, we demonstrate the dissipative property of the Cauchy problem using differential calculus in  H^s_per