Akademik Veri Yönetim Sistemi
Hacettepe Journal of Mathematics and Statistics, cilt.50, sa.2, ss.541-548, 2021 (SCI-Expanded)
This paper studies the following two non-Newtonian equations with nonlinear boundary conditions. Firstly, we show that finite time blow up occurs on the boundary and we get a blow up rate and an estimate for the blow up time of the equation kt = (|kx|r−2 kx)x, (x, t) ∈ (0, L) × (0, T ) with kx(0, t) = kα(0, t), kx(L, t) = kβ (L, t), t ∈ (0, T ) and initial function k (x, 0) = k0 (x), x ∈ [0, L] where r ≥ 2, α, β and L are positive constants. Secondly, we show that finite time blow up occurs on the boundary, and we get blow up rates and estimates for the blow up time of the equation kt = (|kx|r−2 kx)x + kα, (x, t) ∈ (0, L) × (0, T ) with kx(0, t) = 0, kx(L, t) = kβ (L, t), t ∈ (0, T ) and initial function k (x, 0) = k0 (x), x ∈ [0, L] where r ≥ 2, α, β and L are positive constants.