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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)

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
Full Text: DOI
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