Let G =（V, E） be a locally finite connected weighted graph, and ？ be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation ut = ？u ＋ f（u） on G. The blow-up p...Let G =（V, E） be a locally finite connected weighted graph, and ？ be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation ut = ？u ＋ f（u） on G. The blow-up phenomenons for ut = ？u ＋ f（u） are discussed in terms of two cases：（i） an initial condition is given;（ii） a Dirichlet boundary condition is given. We prove that if f satisfies appropriate conditions, then the corresponding solutions will blow up in a finite time.展开更多
In this paper we consider the asymptotic behavior of boundary value problems of nonliner systems εy″= F(t,y,y′,ε) , -1<t<1, y(-1,ε)=A, y(1,ε)=B when F possesses a generalized turning point at t...In this paper we consider the asymptotic behavior of boundary value problems of nonliner systems εy″= F(t,y,y′,ε) , -1<t<1, y(-1,ε)=A, y(1,ε)=B when F possesses a generalized turning point at t=0. The interior layer phenomenon of the problem is discussed.展开更多
基金supported by the National Science Foundation of China(11671401)supported by the Fundamental Research Funds for the Central Universitiesthe Research Funds of Renmin University of China(17XNH106)
文摘Let G =（V, E） be a locally finite connected weighted graph, and ？ be the usual graph Laplacian. In this article, we study blow-up problems for the nonlinear parabolic equation ut = ？u ＋ f（u） on G. The blow-up phenomenons for ut = ？u ＋ f（u） are discussed in terms of two cases：（i） an initial condition is given;（ii） a Dirichlet boundary condition is given. We prove that if f satisfies appropriate conditions, then the corresponding solutions will blow up in a finite time.
文摘In this paper we consider the asymptotic behavior of boundary value problems of nonliner systems εy″= F(t,y,y′,ε) , -1<t<1, y(-1,ε)=A, y(1,ε)=B when F possesses a generalized turning point at t=0. The interior layer phenomenon of the problem is discussed.
