Blow-up Phenomena Of Solutions For Nonlocal Reaction Diffusion Equations With Weighted Term

In recent years,the nonlocal dispersal represented by the integral operator can better describe the propagation phenomena in disciplines such as biology,epidemiology,and material science,and has attracted the attention of many scholars.As one of the important branch of nonlocal diffusion equations,blow-up solutions can be used to describe the instability in the diffusion process of matter.Firstly,we investigated the Blow-up phenomena of solutions for a nonlocal diffusion equation with weighted gradient term under Dirichlet boundary condition.By constructing new auxiliary function and using the differential inequality technique,we derived the bounds of the blow-up time for solutions.Moreover,the existence of global solutions was proved by using Banach fixed point theorem.Secondly,we considered the blow-up solution for a nonlocal diffusion equation with weighted gradient term and positive constant term.The existence of solutions was proved by virtue of the Banach fixed point theorem,by using the differential inequality technique,when positive constant was large enough,then derived bounds for the blow-up time of solutions.Finally,we studied the Blow-up phenomena of solutions for nonlocal diffusion equations with time-dependent coefficients.We established the sufficient conditions to guarantee the existence or blow-up of solutions at finite time,then by using the differential inequality technique,the upper bounds for the blow-up time were obtained.