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Blowup estimates for a semilinear reaction diffusion system. (English) Zbl 0990.35065
The author deals with the problem of blow-up estimates for positive solutions of the semilinear parabolic system: $u_t=\Delta u +u^\alpha v^p,\qquad v_t=\Delta v +u^q v^\beta,$ subject to zero Dirichlet boundary condition on a ball of $$\mathbb{R}^N$$ with nonnegative continuous initial data. The results improve previous work of S. N. Zheng [J. Math. Anal. Appl. 232, 293-311 (1999; Zbl 0935.35042)]. The method of proof relies on the maximum principle.

MSC:
 35K57 Reaction-diffusion equations 35K50 Systems of parabolic equations, boundary value problems (MSC2000) 35B50 Maximum principles in context of PDEs
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References:
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