Blow-up and global existence for semilinear parabolic systems with space-time forcing terms
نویسندگان
چکیده
We investigate the local existence, finite time blow-up and global existence of sign-changing solutions to inhomogeneous parabolic system with space-time forcing terms $$ u_t-\Delta u =|v|^{p}+t^\sigma w_1(x),\,\, v_t-\Delta v =|u|^{q}+t^\gamma w_2(x),\,\, (u(0,x),v(0,x))=(u_0(x),v_0(x)), where $t>0$, $x\in \mathbb{R}^N$, $N\geq 1$, $p,q>1$, $\sigma,\gamma>-1$, $\sigma,\gamma\neq0$, $w_1,w_2\not\equiv0$, $u_0,v_0\in C_0(\mathbb{R}^N)$. For blow-up, two cases are discussed under conditions $w_i\in L^1(\mathbb{R}^N)$ $\int_{\mathbb{R}^N} w_i(x)\,dx>0$, $i=1,2$. Namely, if $\sigma>0$ or $\gamma>0$, we show that (mild) solution $(u,v)$ considered blows up in time, while $\sigma,\gamma\in(-1,0)$, then a occurs when $\frac{N}{2}< \max\left\{\frac{(\sigma+1)(pq-1)+p+1}{pq-1},\frac{(\gamma+1)(pq-1)+q+1}{pq-1}\right\}$. Moreover, $\frac{N}{2}\geq \max\left\{\frac{(\sigma+1)(pq-1)+p+1}{pq-1},\frac{(\gamma+1)(pq-1)+q+1}{pq-1}\right\}$, $p>\frac{\sigma}{\gamma}$ $q>\frac{\gamma}{\sigma}$, is for suitable initial values $w_i$,
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ژورنال
عنوان ژورنال: Chaos Solitons & Fractals
سال: 2021
ISSN: ['1873-2887', '0960-0779']
DOI: https://doi.org/10.1016/j.chaos.2021.110982