TY - JOUR T1 - Well- and Ill-posedness Issues for a Class of 2D Wave Equation with Exponential Growth JO - Journal of Partial Differential Equations VL - 4 SP - 361 EP - 384 PY - 2011 DA - 2011/11 SN - 24 DO - http://doi.org/10.4208/jpde.v24.n4.7 UR - https://global-sci.org/intro/article_detail/jpde/5217.html KW - Nonlinear wave equation KW - well-posedness KW - ill-posedness KW - Moser-Trudinger inequality KW - finite speed of propagation AB -

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.