Blow up for non-Newtonian equations with two nonlinear sources
Küçük Resim Yok
Tarih
2021
Yazarlar
Dergi Başlığı
Dergi ISSN
Cilt Başlığı
Yayıncı
Hacettepe Univ, Fac Sci
Erişim Hakkı
info:eu-repo/semantics/openAccess
Özet
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 k(t) = (vertical bar k(x)vertical bar(r-2) k(x))(x), (x, t) is an element of (0, L) x (0,T) with k(x) (0,t) = k(alpha) (0, t), k(x) (L,t) = k(beta) (L,t), t is an element of (0, T) and initial function k (x, 0) = k(0) (x), x is an element of [0, L] where r >= 2, alpha, beta 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 k(t) = (vertical bar k(x)vertical bar(r-2) k(x))(x) + k(alpha), (x, t) is an element of (0, L) x (0, T) with k(x) (0,t) = 0, k(x) (L,t) = k(beta) (L,t), t is an element of (0,T) and initial function k (x, 0) = k(0) (x), x is an element of [0, L] where r >= 2, alpha, beta and L are positive constants.
Açıklama
Anahtar Kelimeler
heat equation, nonlinear parabolic equation, blow up, maximum principles
Kaynak
Hacettepe Journal of Mathematics and Statistics
WoS Q Değeri
Q3
Scopus Q Değeri
Q3
Cilt
50
Sayı
2
