Global existence and blow-up of solutions of nonlocal diffusion problems with free boundaries?

In this paper, we investigate some nonlocal diffusion problems with free boundaries. We first give the existence and uniqueness of local solution by the ODE basic theory and the contraction mapping principle. Then we provide a complete clas-sification for the global existence and finite time blow-up of solutions. Moreover, estimates of blow-up rate and blow-up time are also obtained for the blow-up solution. (C) 2020 Elsevier Ltd. All rights reserved.

Automated summary

This paper investigates nonlocal diffusion problems with free boundaries, establishing the existence and uniqueness of local solutions using ODE basic theory and the contraction mapping principle. It provides a complete classification for global existence and finite time blow-up of solutions, as well as estimates of blow-up rate and time for the blow-up solution.