Blow-up rate for a semilinear wave equation with exponential   nonlinearity in one space dimension
  We consider in this paper blow-up solutions of the semilinear wave equation in one space dimension, with an exponential source term. Assuming that initial data are in $H^{1}_{loc}\times L^2_{loc}$ or some times in $ W^{1,\infty}\times L^{\infty}$, we derive the blow-up rate near a non-characteristic point in the smaller space, and give some bounds near other points. Our result generalize those proved by Godin under high regularity assumptions on initial data. 
Asma Azaiez, Nader Masmoudi, Hatem Zaag
math.AP