Life span of solutions of a weakly coupled parabolic system |
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| Authors: | Flávio Dickstein Miguel Loayza |
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| Institution: | (1) Instituto de Matemática, Universidade Federal do Rio de Janeiro, Caixa Postal 68530, 21944–970 Rio de Janeiro, R.J., Brazil;(2) Departamento de Matemática, Universidade Federal de Pernambuco, 50740–540 Recife, P.E., Brazil |
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| Abstract: | We consider the Cauchy problem for the weakly coupled parabolic system ∂
t
w
λ−Δ w
λ = F(w
λ) in R
N
, where λ > 0, w
λ = (u
λ, v
λ), F(w
λ) = (v
λ
p
, u
λ
q
) for some p, q ≥ 1, pq > 1, and  , for some nonnegative functions φ1, φ2
C
0(R
N
). If (p, q) is sub-critical or either φ1 or φ2 has slow decay at ∞, w
λ blows up for all λ > 0. Under these conditions, we study the blowup of w
λ for λ small.
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| Keywords: | 35B45 35B30 35B40 35K45 35K57 |
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