Well- and Ill-posedness Issues for a Class of 2D Wave Equation with Exponential Growth

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 H^s(R^2) for s < 1.