Test Function Method Aplied In Nonliear PDEs

By the Test Function method, this paper deals with the nonexistence of global weak solution to PDEs with nonlocal sources. The nonexistence of global weak solution to elliptic equation and the evolution equation, together with the nonexistence of local weak solution to hyperbolic equation is contained in this paper.The main content of this paper is divided into three chapters.In chapter two, we disscuss the nonexistence of global weak solution to elliptic equation with nonlocal sourceswhere ai,j is a Caratheodory function, and . We also give two examples.In chapter two, we consider the nonexistence of global weak solution to evolution equation where a,ij is a Caratheodory function, and . We study this question in two cases: . For these two cases, we give three applications respectively.Chapter four deals with the nonexistence of local weak solution to hyperbolic equationwith . And a necessary condition to the existence of global weak solution of this equation is obtained.