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In this paper, we study the non-global existence of solutions to the following time fractional nonlinear diffusion equations $$\begin{cases} ^cD^{\alpha}_{0|t}u-\Delta u+(1+t)^ru_t=I^{\beta}_{0|t}(|u|^{p-1}u), \ x\in \mathbb{R}^n, \ t>0 \\ u(0,x)=u_0(x), \ u_t(0,x)=u_1(x), \ x\in\mathbb{R}^n, \end{cases}$$ where $1<\alpha<2$, $\beta\in(0,1)$, $1<\alpha+\beta<2$, $r\in (-1,1)$, $p>1$, $u_0, u_1\in L^q(\mathbb{R}^n)(q>1)$ 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].
}, issn = {1746-7659}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jics/22357.html} }In this paper, we study the non-global existence of solutions to the following time fractional nonlinear diffusion equations $$\begin{cases} ^cD^{\alpha}_{0|t}u-\Delta u+(1+t)^ru_t=I^{\beta}_{0|t}(|u|^{p-1}u), \ x\in \mathbb{R}^n, \ t>0 \\ u(0,x)=u_0(x), \ u_t(0,x)=u_1(x), \ x\in\mathbb{R}^n, \end{cases}$$ where $1<\alpha<2$, $\beta\in(0,1)$, $1<\alpha+\beta<2$, $r\in (-1,1)$, $p>1$, $u_0, u_1\in L^q(\mathbb{R}^n)(q>1)$ 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].