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Global boundedness of solutions to a reaction-diffusion system. (English) Zbl 0919.35060

Summary: We obtain the global boundedness of solutions to a Fujita-type reaction-diffusion system of the type \[ u_t- d_1\Delta u= b_1 u^{p_1} v^{q_1},\quad v_t- d_2\Delta v= b_2 u^{p_2} v^{q_2},\quad (x,t)\in\Omega\times \mathbb{R}_+. \] This global boundedness results from diffusion effect, homogeneous Dirichlet boundary value conditions and appropriate reactions.

MSC:

35K57 Reaction-diffusion equations
35B35 Stability in context of PDEs
35K50 Systems of parabolic equations, boundary value problems (MSC2000)
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