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Zbl 1212.35225
Aoyagi, Yutaka; Tsutaya, Kimitoshi; Yamauchi, Yusuke
Global existence of solutions for a reaction-diffusion system. (English)
[J] Differ. Integral Equ. 20, No. 12, 1321-1339 (2007). ISSN 0893-4983

Summary: We show the global existence of solutions of a reaction-diffusion system with the nonlinear terms $\vert x\vert ^{\sigma _j}u^{p_j}v^{q_j}$. 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 super linear case by contraction argument. Our conditions for the global existence are optimal in view of the nonexistence results proved by {\it Y. Yamauchi}(to appear in Methods Appl.\ Anal.).

MSC 2000:: *35K57 Reaction-diffusion equations
35B33 Critical exponents
35K05 Heat equation
35K45 Systems of parabolic equations, initial value problems

Keywords: reaction-diffusion system; existence; uniqueness; supersolution; comparison principle

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