Abstract
Extending the previous work [1], we establish well-posedness results for a more general class of semilinear wave equations with exponential growth. First, we investigate the well-posedness in the energy space. Then, we prove the propagation of the regularity in the Sobolev spaces H-s(R-2) with s >= 1. Finally, an ill-posedness result is obtained in Hs(R-2) for s < 1.