Application of the Faedo-Galerkin method to a semilinear wave equation with localized dissipation

Authors

  • Carlos Alberto Peña Miranda Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Calle Germán Amézaga No 375 - Edificio Jorge Basadre, Lima-Perú. http://orcid.org/0000-0002-4339-4615
  • Alfonso Pérez Salvatierra Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Calle Germán Amézaga No 375 - Edificio Jorge Basadre, Lima-Perú. http://orcid.org/0000-0001-9944-4020

DOI:

https://doi.org/10.17268/sel.mat.2020.02.02

Keywords:

Faedo-Galerkin Method, existence and uniqueness of solution, semilinear wave equation, localized dissipation

Abstract

In this article, we demonstrate the unique existence of the solution for the semilinear wave equation with localized dissipation using the Faedo-Galerkin method.

Author Biographies

Carlos Alberto Peña Miranda, Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Calle Germán Amézaga No 375 - Edificio Jorge Basadre, Lima-Perú.

Departamento Academico de Matematica

Alfonso Pérez Salvatierra, Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Calle Germán Amézaga No 375 - Edificio Jorge Basadre, Lima-Perú.

Departamento Academico de Matematica

References

Coddington E, Levinson N. Theory of Ordinary Differential Equations. New York: Mac Graw-Hill; 1955.

Lions JL. Quelques Méthodes de Résolution des Problémes Aux Limites Non Linéaires. Paris: Dunod; 1969.

Lions JL, Magenes E. Problémes aux Limites nom Homogens et Applications. Vol 1. Paris: Dumod; 1968.

Milla M. Análise Espectral em Espacos de Hilbert, Textos de Métodos Matemáticos. Vol 28. Rio de Janeiro: IM-UFRJ; 1994.

Nakao M. A difference inequality and its applications to nonlinear evolution equations. J. Math. Soc. Japan. 1978; 30(4):747-

Nakao M. Decay estimate of the solutions to the initial – boundary value problem for the wave equation with a dissipation. Israel J. Mathematics. 1996; 95:25-42.

Peña C, Pérez A, Guardia A. Decaimiento exponencial de la ecuación de onda semilineal con disipación localizada. Pesquimat. 2013; 16(1):19-34.

Zuazua E. Stability and decay for a class of nonlinear hyperbolic problems. Asymptotic Analysis. 1988; 1(2):161-185.

Zuazua E. Exponential decay for the semilinear wave equation with locally distributed damping. Comm. Partial Differential Equations. 1990; 15(2):205-235.

Zuazua E. Exponential decay for the semilinear wave equations, with localized Damping in Unbounded Domains. J. Math. Pures Appl. 1991; 70(4):513-529.

Published

2020-12-25

How to Cite

Peña Miranda, C. A., & Pérez Salvatierra, A. (2020). Application of the Faedo-Galerkin method to a semilinear wave equation with localized dissipation. Selecciones Matemáticas, 7(02), 202-213. https://doi.org/10.17268/sel.mat.2020.02.02

Most read articles by the same author(s)