Differential and Integral Equations

Global existence of solutions for a reaction-diffusion system

Yutaka Aoyagi, Kimitoshi Tsutaya, and Yusuke Yamauchi

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text


We show the global existence of solutions of a reaction-diffusion system with the nonlinear terms $|x|^{\sigma_j}u^{p_j}v^{q_j}$. The proof is based on the existence of supersolutions and the comparison principle. We also prove that uniqueness of the global solutions holds in the superlinear case by contraction argument. Our conditions for the global existence are optimal in view of the nonexistence results proved by Yamauchi [12].

Article information

Differential Integral Equations, Volume 20, Number 12 (2007), 1321-1339.

First available in Project Euclid: 20 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 35K57
Secondary: 35B33 35K05 35K45


Aoyagi, Yutaka; Tsutaya, Kimitoshi; Yamauchi, Yusuke. Global existence of solutions for a reaction-diffusion system. Differential Integral Equations 20 (2007), no. 12, 1321--1339. https://projecteuclid.org/euclid.die/1356039068

Export citation