Asymptotic Behavior and Decay Estimates of the Solutions for a Nonlinear   Parabolic Equation with Exponential Nonlinearity
  We consider a nonlinear parabolic equation with an exponential nonlinearity which is critical with respect to the growth of the nonlinearity and the regularity of the initial data. After showing the equivalence of the notions of weak and mild solutions, we derive decay estimates and the asymptotic behavior for small global-in-time solutions. 
Giulia Furioli, Tatsuki Kawakami, Bernhard Ruf, Elide Terraneo
math.AP