Global existence and blowup of a nonlocal problem in space with free boundary

@article{Zhou2012GlobalEA,
title={Global existence and blowup of a nonlocal problem in space with free boundary},
author={P. Zhou and Zhigui Lin},
journal={Journal of Functional Analysis},
year={2012},
volume={262},
pages={3409-3429}
}

Abstract This paper concerns a double fronts free boundary problem for the reaction–diffusion equation with a nonlocal nonlinear reaction term in space. For such a problem, we mainly study the blowup property and global existence of the solutions. Our results show that if the initial value is sufficiently large, then the blowup occurs, while the global fast solution exists for a sufficiently small initial data, and the intermediate case with a suitably large initial data gives the existence of… Expand