Existence and Regularity of the Solution of Non homogeneous Schrödinger Equation in Periodic Sobolev Spaces

• Autores: Santiago Ayala, Yolanda, Rojas Romero, Santiago
• Formato: artículo
• Fecha de Publicación: 2021
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revistas - Universidad Nacional de Trujillo
• Lenguaje: español
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/3700
• Enlace del recurso: https://revistas.unitru.edu.pe/index.php/SSMM/article/view/3700
• Nivel de acceso: acceso abierto
• Materia: Teoría de grupos; ecuación de Schrödinger; ecuación no homogénea; espacios de Sobolev periódico; Teoría de Fourier; Groups theory; Schrödinger equation; non homogeneous equation; Periodic Sobolev spaces; Fourier theory

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.