Existence and continuous dependence of solution of the Boussinesq wave equation in periodic Sobolev spaces

• Autores: Papuico Bernardo, Victor, Santiago Ayala, Yolanda
• Formato: artículo
• Fecha de Publicación: 2020
• Institución: Universidad Nacional de Trujillo
• Repositorio: Revistas - Universidad Nacional de Trujillo
• Lenguaje: español
• OAI Identifier: oai:ojs.revistas.unitru.edu.pe:article/2958
• Enlace del recurso: https://revistas.unitru.edu.pe/index.php/SSMM/article/view/2958
• Nivel de acceso: acceso abierto
• Materia: Family of strongly continuous operators; Boussinesq equation; Fourier Theory; Periodic Sobolev spaces; Familia de Operadores fuertemente continuos; ecuación Boussinesq; Teoría de Fourier; Espacios de Sobolev periódicos

We will begin our study, focusing on the theory of periodic Sobolev spaces, for this we cite [1]. Then, we will prove that the non-homogeneous Boussinesq equation has a local solution and that the solution also continually depends on the initial data and non-homogeneity, we do this intuitively using Fourier theory and in an elegant version introducing families of strongly continuous operators, inspired by the work of Iorio [1], Santiago and Rojas [4], [3] and [2].