@article{Li2022, 
author = {Zhiqiang Li},
title = {The finite time blow-up for Caputo-Hadamard fractional diffusion equation involving nonlinear memory},
year = {2022},
journal = {AIMS Mathematics},
volume = {7},
number = {7},
pages = {12913-12934},
keywords = {Caputo-Hadamard derivative, fractional Laplacian, nonlinear memory, finite time blow-up, fixed point argument},
url = {https://www.sciopen.com/article/10.3934/math.2022715},
doi = {10.3934/math.2022715},
abstract = {In this article, we focus on the blow-up problem of solution to Caputo-Hadamard fractional diffusion equation with fractional Laplacian and nonlinear memory. By virtue of the fundamental solutions of the corresponding linear and nonhomogeneous equation, we introduce a mild solution of the given equation and prove the existence and uniqueness of local solution. Next, the concept of a weak solution is presented by the test function and the mild solution is demonstrated to be a weak solution. Finally, based on the contraction mapping principle, the finite time blow-up and global solution for the considered equation are shown and the Fujita critical exponent is determined. The finite time blow-up of solution is also confirmed by the results of numerical experiment.}
}