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On the blow-up of solutions of a convective reaction diffusion equation

  • J. Aguirre (a1) and M. Escobedo (a1)

Synopsis

We study the blow-up of positive solutions of the Cauchy problem for the semilinear parabolic equation

where u is a scalar function of the spatial variable x ∈ ℝN and time t > 0, a ∈ ℝV, a ≠ 0, 1 < p and 1 ≦ q. We show that: (a) if p > 1 and 1 ≦ qp, there always exist solutions which blow up in finite time; (b) if 1 < qp ≦ min {1 + 2/N, 1 + 2q/(N + 1)} or if q = 1 and 1 < p ≦ l + 2/N, then all positive solutions blow up in finite time; (c) if q > 1 and p > min {1 + 2/N, 1 + 2q/N + 1)}, then global solutions exist; (d) if q = 1 and p > 1 + 2/N, then global solutions exist.

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On the blow-up of solutions of a convective reaction diffusion equation

  • J. Aguirre (a1) and M. Escobedo (a1)

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