Existence Of Global Solutions For A Semilinear Reaction-Diffusion System

This thesis is concerned with the global existence of nonnegative solutions of the following reaction-diffusion system where N≥1, p, q> 0,u0(x),v0(x) are nonnegative continuous bounded functions on RN and 0 (?) a(x) € Ca(RN) with 0< a< 1 and a(x) (?). We obtain the following results:If 0<pq≤1, every nonnegative solution of the system is global; If pq>1, m≥0, when max ,the system does not have global solutions for any nontrivial initial data; when max the system exists global solutions for sufficiently small initial data. Some initial criteria of global solutions when m<0 are also established. The results extend that of Escobedo and Herrero in JDE 1991.