@Article{JICS-17-003,
author = {Qian , Qian and Li , Yaning},
title = {The Nonexistence of Global Solutions for a Damped Time Fractional Diffusion Equation with Nonlinear Memory},
journal = {Journal of Information and Computing Science},
year = {2024},
volume = {17},
number = {1},
pages = {003--018},
abstract = {<p style="text-align: justify;">In this paper, we study the non-global existence of solutions to the following time fractional
nonlinear diffusion equations
$$\begin{cases} ^cD^{\alpha}_{0|t}u-\Delta u+(1+t)^ru_t=I^{\beta}_{0|t}(|u|^{p-1}u), \ x\in \mathbb{R}^n, \ t&gt;0 \\ u(0,x)=u_0(x), \ u_t(0,x)=u_1(x), \ x\in\mathbb{R}^n, \end{cases}$$ where $1&lt;\alpha&lt;2$, $\beta\in(0,1)$, $1&lt;\alpha+\beta&lt;2$, $r\in (-1,1)$, $p&gt;1$, $u_0, u_1\in L^q(\mathbb{R}^n)(q&gt;1)$ and $^cD^{\alpha}_{0|t}u$ denotes left Caputo fractional derivative of order $\alpha$. By using the test function method, we prove that
the problem admits no global weak solution with suitable initial data when $p$ falls in different intervals. Our
results generalize that in [4].</p>},
issn = {1746-7659},
doi = {https://doi.org/},
url = {http://global-sci.org/intro/article_detail/jics/22357.html}
}