Electron. J. Differential Equations, Vol. 2017 (2017), No. 279, pp. 1-11.

Well-posedness and exponential stability for a wave equation with nonlocal time-delay condition

Carlos A. Raposo, Hoang Nguyen, Joilson O. Ribeiro, Vanessa Barros

Well-posedness and exponential stability of nonlocal time-delayed of a wave equation with a integral conditions of the 1st kind forms the center of this work. Through semigroup theory we prove the well-posedness by the Hille-Yosida theorem and the exponential stability exploring the dissipative properties of the linear operator associated to damped model using the Gearhart-Huang-Pruss theorem.

Submitted July 24, 2017. Published November 10, 2017.
Math Subject Classifications: 35L05, 35B35, 35L51.
Key Words: Well-posedness; exponential stability; wave equation; semigroup.

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Carlos Alberto Raposo
Departamento de Matemática e Estatística
Universidade Federal de São João del-Rei, Brazil
email: raposo@ufsj.edu.br
Huy Hoang Nguyen
Instituto de Matemática and Campus de Xerém
Universidade Federal do Rio de Janeiro, Brazil
email: nguyen@im.ufrj.br
Joilson Oliveira Ribeiro
Instituto de Matemática
Universidade Federal da Bahia, Brazil
email: joilsonor@ufba.br
Vanessa Barros de Oliveira
Instituto de Matemática
Universidade Federal da Bahia, Brazil
email: vbarrosoliveira@gmail.com

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