TY  - JOUR
AU  - Li, Zhiqiang
PY  - 2022
TI  - The finite time blow-up for Caputo-Hadamard fractional diffusion equation involving nonlinear memory
JO  - AIMS Mathematics
SP  - 12913
EP  - 12934
VL  - 7
IS  - 7
AB  - 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.
UR  - https://doi.org/10.3934/math.2022715
DO  - 10.3934/math.2022715