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Life span of solutions with large initial data for a semilinear parabolic system. (English) Zbl 1219.35027
The author investigates the initial-boundary value problem $$u_t=\Delta u-v^q$$, $$v_t=\Delta v-u^q$$ in $$\Omega\times (0,T)$$, $$u(x,t)=v(x,t)=0$$ on $$\partial\Omega\times (0,T)$$, $$u(x,0)= \rho\varphi$$, $$v(x,0)= \rho\psi$$ in $$\Omega$$, where $$p,q \geq 1$$ and $$pq>1$$, $$\Omega$$ is a bounded domain in $$\mathbb R^n$$ with a smooth boundary $$\partial \Omega$$, $$\rho>0$$ is a parameter, and $$\varphi (x)$$ and $$\psi (x)$$ are nonnegative continuous functions on $$\overline{\Omega}$$.
Reviewer: Jiaqi Mo (Wuhu)

##### MSC:
 35B44 Blow-up in context of PDEs 35K57 Reaction-diffusion equations 35K51 Initial-boundary value problems for second-order parabolic systems 35K58 Semilinear parabolic equations
##### Keywords:
life span; blow-up; semilinear parabolic system
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##### References:
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