# American Institute of Mathematical Sciences

October  1998, 4(4): 635-640. doi: 10.3934/dcds.1998.4.635

## The linear damped wave equation, Hamiltonian symmetry, and the importance of being odd

 1 Departamento de Matemática, Instituto Superior Técnico, Av.Rovisco Pais, 1096 Lisboa Codex, Portugal

Received  September 1997 Revised  March 1998 Published  July 1998

We show the existence and fully characterize a class of dissipative perturbations of the linear wave equation for which the spectrum of the associated linear operator has Hamiltonian symmetry and the energy of finite-energy solutions neither decays to zero nor grows to infinity, but instead oscillates and remains bounded for all time.
Citation: Pedro Freitas. The linear damped wave equation, Hamiltonian symmetry, and the importance of being odd. Discrete and Continuous Dynamical Systems, 1998, 4 (4) : 635-640. doi: 10.3934/dcds.1998.4.635
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