Blow-up for a parabolic system coupled in an equation and a boundary condition

ISSN： 1473-7124

Source： Proceedings Section A: Mathematics - Royal Society of Edinburgh, Vol.131, Iss.6, 2001-12, pp. : 1345-1355

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Abstract

In this paper, we consider non-negative solutions ofu_t = Δu + v^p, v_t = Δv in Ω × (0,∞),∂u/∂ν = 0, ∂v/∂ν = u^q on ∂Ω × (0,∞),u(x, 0) = u₀(x), v(x, 0) = v₀(x) in Ω.We prove that if pq ≤ 1, every solution is global while if pq > 1, all solutions blow up in finite time. We also show that if p, q ≥ 1, then blow-up can occur only on the boundary.

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