A Necessary and Sufficient Condition for Global Existence for a Quasilinear Reaction-diffusion System

We show that the reaction-diffusion system ut=Δφ(u)+f(v), vt=Δψ(v)+g(u), with homogeneous Neumann boundary conditions, has a positive global solution on Ω×[0,∞) if and only if ∫∞ds/f(F−1(G(s)))=∞ (or, equivalently, ∫∞ds/g(G−1(F(s)))=∞), where F(s)=∫0sf(r)dr and G(s)=∫0sg(r)dr. The domain Ω⊆ℝN(N≥1) i...

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