Electronic Journal of Differential Equations,
Conference 06 (2001), pp. 45-53.

Title: First moments of energy and convergence to equilibrium. 

Authors: Jerome Busca (Univ. Francois Rabelais, Tours,  France)
 
Abstract: 
  A basic question is to establish 
  convergence to equilibrium for globally defined 
  solutions to evolution problems. The purpose here 
  is to emphasize the role of symmetry. In particular, 
  it is proved that in some cases the {\em first moments of energy} are 
  constant on the $\omega$-limit set of the solution. This 
  key property is used to prove convergence in two model 
  evolution problems. This communication 
  is based on two joint works with P. Felmer \cite{busca_felmer} 
  and M.A. Jendoubi, P. Polacik \cite{busca_jendoubi}.

Published January 8, 2001.
Math Subject Classifications: 35B50, 35A05.
Key Words: Parabolic Equations; Equilibrium; Convergence.