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.
Categories: math.AP