半线性拟双曲型积分微分方程的初边值问题和初值问题

ON THE INITIAL BOUNDARY VALUE PROBLEM AND INITIAL VALUE PROBLEM FOR THE SEMILINEAR PSEUDO-HYPERBOLIC INTEGRO-DIFFERENTIAL EQUATION

本文讨论半线性拟双曲型积分微分方程的初边值和初值问题。用积分方程的理论和Ｇａｌｅｒｋｉｎ方法证明了问题的整体强解的存在性。

The initial boundary value problem and initial value problem for the semilinear pseudo-hyperbolic integrodifferential equation are considered. The existence, uniqueness and regularities of the global strongly solution of the problems are proved by the theory of integral equations and the Galerkin method.