一类高阶多变量的非线性伪双曲方程组的周期边值问题与初值问题

THE PERIODIC-BOUNDARY VALUE PROBLEM AND INITIAL VALUE PROBLEM FOR A NONLINEAR HIGHER ORDER PSEUDO-HYPER BOLIC SYSTEMS

本文利用能量积分估计Leray—Schauder不动点证明了一类高阶多变量的非线性伪双曲方程组的周期边值问题和初值问题广义解的存在性与唯一性.

In this paper, the follouing periodic - boundary value problem (1.1), ( l . 2 ) and in i t ia l value problem (1.1 )、(1.3) Where u= (u1, …,uN) ,g= ( gi(x,t),…, gN (x, t) ) , A(x, f) = (a ij(x, t) ) N ,XN are studied. By useing the energy intcgral estimates and the Leray-Schauder fixed point theorem, the existana and uniqueness of the generalized solution for problems ( 1. 1 )、 (1.2) and (1.1)、( 1.3 ) are proved.