图上无界拉普拉斯算子非线性抛物方程解的存在性和爆破现象OA

In this paper,we study the existence and blow-up of solutions to a nonlinear parabolic equation with unbounded Laplace operators on locally finite graphs:ut=Δu+h(x)f(u(x,t)).First,the existence and uniqueness of mild solutions in a short time interval are established using the Banach fixed-point theorem.Then,by skillfully constructing auxiliary functions and under appropriate conditions concerning polynomial growth of the graph and the nonlinearity f,the finite-time blow-up of mild solutions is proved via heat kernel estimates.These results extend those in the literature[13].