An explicit Lyapunov function for reflection symmetric parabolic partial differential equations on the circle (Q2925748)

The work continues the authors' research related to character and structure of the dynamics on the global attractors of parabolic equations considered in their scalar form. One of the key issues of the research is connected with existence and non-existence of Lyapunov functions. The authors construct a Lyapunov function for the equations with periodic boundary conditions. To do so, they make use of the method suggested in 1988 by H.~Matano. In the conclusive part of the paper, the authors discuss the problem of global attractors for some classes of partial differential equations.