We consider a nonlocal parabolic and the corresponding elliptic equation with exponential nonlinearity. At first, we study the set of a stationary solution and compute its Morse index. Next, we obtain the time-global solution in the use of the Lyapunov function and define the dynamical system. Finally, we construct an exponential attractor by a squeezing property.
Tosiya Miyasita. "A dynamical system for a nonlocal parabolic equation with exponential nonlinearity." Rocky Mountain J. Math. 45 (6) 1897 - 1917, 2015. https://doi.org/10.1216/RMJ-2015-45-6-1897