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

作　　者：MAHOUACHI Olfa SAANOUNI Tarek 

机构地区：[1]Laboratoire d＇e＇quations aux de＇rivdes partielles et applications Faculte＇ des Sciences deTunis, De＇partement de Mathe＇matiques Campus universitaire 1060, Tunis, Tunisie.

出　　处：《Journal of Partial Differential Equations》2011年第4期361-384,共24页偏微分方程（英文版）

摘　　要：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 HS（IR^2） with s 〉 1. Finally, an ill-posedness result is obtained in HS（IR^2） for s 〈 1.

关 键 词：Nonlinear wave equation WELL-POSEDNESS ILL-POSEDNESS Moser-Trudinger inequality finite speed of propagation. 

分 类 号：O175.29[理学—数学] O151.21[理学—基础数学]