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The FaberKrahn inequality for random/nonautonomous parabolic equations
Trajectory and global attractors of dissipative hyperbolic equations with memory
1.  Institute for Problems of Information Transmission, Russian Academy of Sciences, Bolshoy Karetniy 19, Moscow 101447, GSP4, Russian Federation 
2.  Laboratoire d'Applications des Mathématiques  SP2MI, Boulevard Marie et Pierre Curie  Téléport 2, Chasseneuil Futuroscope Cedex 
As an application, we construct trajectory and global attractors for dissipative hyperbolic equations with linear memory. We also prove the existence of a global Lyapunov function for the dissipative hyperbolic equation with memory. The existence of such a Lyapunov function implies a regular structure for the trajectory and global attractors of the equation under consideration.
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