TY - JOUR
T1 - Well- and Ill-posedness Issues for a Class of 2D Wave Equation with Exponential Growth
AU - Olfa Mahouachi  & Tarek Saanouni 
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 - <p>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 &lt; 1.</p>