# American Institute of Mathematical Sciences

2003, 2003(Special): 182-188. doi: 10.3934/proc.2003.2003.182

## Blow-up estimates of positive solutions of a reaction-diffusion system

 1 Department of Mathematics, Christopher Newport University, Newport News, VA 23606, United States

Received  September 2002 Revised  April 2003 Published  April 2003

This paper is concerned with positive solutions of the reaction-diffusion system

$u_t - \Delta u = u^(m_1)v^(n_1)$ ,
$v_t - \Delta v = u^(m_2)v^(n_2)$ ,

which blow up at $t = T$. We obtain the following estimates on the blow-up rates:

$c(T - t)^(-(n_1-n_2+1)/\gamma) <= max_(x\in\Omega) u(x, t) <= C(T - t)^(-(n_1-n_2+1)/\gamma)$,
$c(T - t)^(-(m_2-m_1+1)/\gamma) <= max_(x\in\Omega) v(x, t) <= C(T - t)^(-(m_2-m_1+1)/\gamma)$,

for some positive constants $c,C$ and $\gamma = m_2n_1 - (1 - m_1)(1 - n_2)$.

Citation: Hongwei Chen. Blow-up estimates of positive solutions of a reaction-diffusion system. Conference Publications, 2003, 2003 (Special) : 182-188. doi: 10.3934/proc.2003.2003.182
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