@article{Gao2022, 
author = {Peng Gao and Pengyu Chen},
title = {Blowup and MLUH stability of time-space fractional reaction-diffusion equations},
year = {2022},
journal = {Electronic Research Archive},
volume = {30},
number = {9},
pages = {3351-3361},
keywords = {time-space fractional reaction-diffusion equations, Sobolev space, saturated mild solutions, local uniqueness, blowup alternative result},
url = {https://www.sciopen.com/article/10.3934/era.2022170},
doi = {10.3934/era.2022170},
abstract = {In this paper, we consider a class of nonlinear time-space fractional reaction-diffusion equations by transforming the time-space fractional reaction-diffusion equations into an abstract evolution equations in a fractional Sobolev space. Based on operator semigroup theory, the local uniqueness of mild solutions to the reaction-diffusion equations is obtained under the assumption that nonlinear function is locally Lipschitz continuous. On this basis, a blowup alternative result for unique saturated mild solutions is obtained. We further verify the Mittag-Leffler-Ulam-Hyers stability of the nonlinear time-space fractional reaction-diffusion equations.}
}