Existence and regularity of solution of the heat equation in periodic Sobolev spaces - Santiago Ayala, Yolanda (2019)
In this article we prove that the Cauchy problem associated to the heat equation in periodic Sobolev spaces is well posed. We do this in an intuitive way using Fourier theory and in a fine version using Semigroups theory, inspired by works Iorio [1] and Santiago and Rojas [3]. Also, we study the relationship between the initial data and differentiability of the solution.Finally, we study the corresponding nonhomogeneous problem and prove it is locally well posed and even more we obtain the continuous dependence of the solution with respect to the initial data and the non homogeneity.