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Non-simultaneous blow-up in a semilinear parabolic system. (English) Zbl 0990.35057
Consider the system of parabolic equations: \[ u_t=\Delta u+u^{p_{11}}v^{p_{12}},\qquad v_t=\Delta v+u^{p_{21}}v^{p_{22}}, \] on \(\mathbb{R}^N\) with positive bounded initial data. In this paper the authors study the range of parameters for which non-simultaneous blow-up of solutions may occur. The results are based on the knowledge of the blow-up range found in [M. Escobedo and H. A. Levine, Arch. Ration. Mech. Anal. 129, 47-100 (1995; Zbl 0822.35068)].

MSC:
35K45 Initial value problems for second-order parabolic systems
35K57 Reaction-diffusion equations
35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs
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