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

35K57Reaction-diffusion equations
35B33Critical exponents (PDE)
35K05Heat equation
35K45Systems of second-order parabolic equations, initial value problems