一类高阶多维非线性伪双曲方程

A Class of Multidimensional Nonlinear Pseudo-hyperbolic Equations of Higher Order

中文关键词:  能量积分  Sobolcv嵌入定理  Lcary－Schauder不动点定理  整体广义解。

英文关键词:energy integral  sobolev imbedding theorems  Leary-Schauder fixed point the-orem  global generalized solutions。

中文摘要:

      本文研究了一类高阶多维非线性伪双曲方程，通过先验估计结合Ｓｏｂｏｌｅｖ嵌入定理及Ｌｃａｒｙ－Ｓｃｈａｕｄｅｒ不动点定现证明了初边值问题整体广义解的存在性和唯一性。

英文摘要:

      This paper discusses a class of multidimensional nonlinear pseudo-hyperbolic equationsof higher order by presenting priori estimate,Sobolev imbedding theorems and Leary-Schauder fixed point theorem。 The existence and uniqueness of the initial boundary valueproblem are also demonstrated。