Existence of solution and its behavior with respect to one parameter for a wave model in a viscous fluid

• Autores: Milla Garcia, Luis, Santiago Ayala, Yolanda
• Formato: artículo
• Fecha de Publicación: 2020
• Institución: Universidad Nacional Mayor de San Marcos
• Repositorio: Revista UNMSM - Pesquimat
• Lenguaje: español
• OAI Identifier: oai:ojs.csi.unmsm:article/18442
• Enlace del recurso: https://revistasinvestigacion.unmsm.edu.pe/index.php/matema/article/view/18442
• Nivel de acceso: acceso abierto
• Materia: Existence of solution; KdV-Kuramoto-Sivashinski equation; periodic Sobolev spaces; Semigroups; Existencia de solución; ecuación KdV-Kuramoto-Sivashinski; espacios de Sobolev periódico; Semigrupos

In this work we study the existence, uniqueness and continuous dependence of the solution of the KdV-Kuramoto-Sivashinsky homogeneous linear equation in periodic Sobolev spaces. We do this using semigroup theory and Fourier theory on periodic distributions. Also, using the immersions between the Sobolev spaces we obtain regularity additional properties. Furthermore, we proved some claims done in [8].Finally, we analyze the behavior of the solution with respect to one parameter, proving that its limit is the solution of a Cauchy problem whose associated semigroup is the restriction of a group.