# American Institute of Mathematical Sciences

March  2012, 2(1): 17-28. doi: 10.3934/mcrf.2012.2.17

## Eventual regularity of a wave equation with boundary dissipation

 1 Department of Mathematics, Zhejiang University, Hangzhou 310027, China 2 School of Mathematics and Statistics, Northeast Normal University, Changchun 130024, China 3 Institut de Recherche Mathématique Avancée, Université Louis Pasteur de Strasbourg, 7 rue René-Descartes, 67084 Strasbourg

Received  March 2011 Revised  October 2011 Published  January 2012

This paper addresses a study of the eventual regularity of a wave equation with boundary dissipation and distributed damping. The equation under consideration is rewritten as a system of first order and analyzed by semigroup methods. By a certain asymptotic expansion theorem, we prove that the associated solution semigroup is eventually differentiable. This implies the eventual regularity of the solution of the wave equation.
Citation: Kangsheng Liu, Xu Liu, Bopeng Rao. Eventual regularity of a wave equation with boundary dissipation. Mathematical Control & Related Fields, 2012, 2 (1) : 17-28. doi: 10.3934/mcrf.2012.2.17
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