Global existence of solutions for a reaction-diffusion system. (English) Zbl 1212.35225

Aoyagi, Yutaka; Tsutaya, Kimitoshi; Yamauchi, Yusuke

Differ. Integral Equ. 20, No. 12, 1321-1339 (2007).

Summary: 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 super linear case by contraction argument. Our conditions for the global existence are optimal in view of the nonexistence results proved by Y. Yamauchi(to appear in Methods Appl.Anal.).

MSC:

35K57	Reaction-diffusion equations
35B33	Critical exponents in context of PDEs
35K05	Heat equation
35K45	Initial value problems for second-order parabolic systems

Keywords:

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