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 & Continuous Dynamical Systems, 1998, 4 (4) : 635-640. doi: 10.3934/dcds.1998.4.635
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