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2007 Global existence of solutions for a reaction-diffusion system
Yutaka Aoyagi, Kimitoshi Tsutaya, Yusuke Yamauchi
Differential Integral Equations 20(12): 1321-1339 (2007).

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].

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Yutaka Aoyagi. Kimitoshi Tsutaya. Yusuke Yamauchi. "Global existence of solutions for a reaction-diffusion system." Differential Integral Equations 20 (12) 1321 - 1339, 2007.

Information

Published: 2007
First available in Project Euclid: 20 December 2012

zbMATH: 1212.35225
MathSciNet: MR2377020

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

Rights: Copyright © 2007 Khayyam Publishing, Inc.

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Vol.20 • No. 12 • 2007
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