Abstract: This paper considers the blow-up phenomena of solutions for nonlocal diffusion equations with a weighted gradient reaction, and gives the sufficient conditions for existence and blow-up. Firstly, the local existence of solutions is proven by using the Banach fixed-point theorem. Secondly, a new auxiliary function is constructed by using eigenfunctions. Finally, the results are combined with the differential inequality technique to obtain the upper bound of the blow-up time.

Key words: weight function, gradient reaction, nonlocal diffusion, blow-up