Existence of the solution of a Schrödinger type homogeneous model in periodic Sobolev spaces
DOI:
https://doi.org/10.17268/sel.mat.2022.02.11Keywords:
Unitary groups theory, Schrödinger type equation, homogeneous equation, periodic Sobolev spaces, Fourier theoryAbstract
In this article we prove that the Cauchy problem associated to a Schrödinger type homogeneous model in periodic Sobolev spaces is well posed. We do this in an intuitive way using Fourier theory and in a fine version using Groups theory, inspired by works Iorio [3], Santiago and Rojas [10] and [11]. Finally, we study the relationship between initial data and differentiability of the solution.
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