## Differential and Integral Equations

### Global existence of solutions for a reaction-diffusion system

#### Abstract

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

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

Dates
First available in Project Euclid: 20 December 2012

https://projecteuclid.org/euclid.die/1356039068

Mathematical Reviews number (MathSciNet)
MR2377020

Zentralblatt MATH identifier
1212.35225

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

#### Citation

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