Existence and Regularity of the Solution of Non homogeneous Schrödinger Equation in Periodic Sobolev Spaces
DOI:
https://doi.org/10.17268/sel.mat.2021.01.04Keywords:
Groups theory, Schrödinger equation, non homogeneous equation, Periodic Sobolev spaces, Fourier theoryAbstract
In this articlewe prove that the Cauchy problemassociated to the Schrödinger equation in periodic Sobolev spaces is well posed. We do this in an intuitiveway using Fourier theory and in a fine version using Groups theory, inspired by works Iorio [3], Santiago and Rojas [12] and [13]. Also, we study the relationship between initial data and differentiability of the solution.
Finally, we study the corresponding non-homogeneous problemand prove that it is locallywell posed, and that the solution has continuous dependence with respect to the initial data and the non-homogeneity in compact intervals.
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Copyright (c) 2021 Yolanda Santiago Ayala, Santiago Rojas Romero
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