Tokyo Journal of Mathematics

The Life Span of Blow-up Solutions for a Weakly Coupled System of Reaction-Diffusion Equations

Yasumaro KOBAYASHI

Abstract

We consider the weakly coupled system of reaction-diffusion equations $u_t=\Delta u+|x|^{\sigma_1}v^p, \quad v_t=\Delta v+|x|^{\sigma_2}u^q ,$ $u(x,0)=\lambda^\mu\varphi(x), \quad v(x,0)=\lambda^\nu\psi(x)$ where $x\in\mathbf{R}^N$, $t>0$, $p$, $q>1$ and $0\leq\sigma_1<N(p-1)$, $0\leq\sigma_2<N(q-1)$. The existence of solutions, blow-up conditions, and global solutions of the above equations are studied by Mochizuki-Huang. In this paper, we consider the estimate of maximal existence time of blow-up solutions in $I^{\delta_1}\times I^{\delta_2}$ as $\lambda$ goes to 0 or $\infty$.

Article information

Source
Tokyo J. Math., Volume 24, Number 2 (2001), 487-498.

Dates
First available in Project Euclid: 19 October 2009

https://projecteuclid.org/euclid.tjm/1255958189

Digital Object Identifier
doi:10.3836/tjm/1255958189

Mathematical Reviews number (MathSciNet)
MR1874985

Zentralblatt MATH identifier
1200.35171

Citation

KOBAYASHI, Yasumaro. The Life Span of Blow-up Solutions for a Weakly Coupled System of Reaction-Diffusion Equations. Tokyo J. Math. 24 (2001), no. 2, 487--498. doi:10.3836/tjm/1255958189. https://projecteuclid.org/euclid.tjm/1255958189